I also don't think there's a singular answer there because goalies are wired differently (even intra-species)...like, I wonder aloud about Patrick Roy playing behind some good defenses and, frankly, I don't think he gets enough discredit for some really putrid goals that he's given up in the playoffs over the years (of course, bound to happen to anyone when you play two zillion playoff games, but...) - I wonder if there's any tie to, say, not seeing a scoring chance for six minutes and then Cam Neely blows one by him from 45 feet...
Having seen the vast majority of Fleury's career, he certainly seemed to be more engaged when he was under siege against all odds...like game 5 of the 2008 Final, for instance...but he's notoriously not focused when he doesn't see pucks. In fact, I'd bet a round of drinks on Fleury being the all-time leader in giving up goals on the first shot of the game...at least in my lifetime...I don't know if Murray Bannerman or someone from the lean years is maybe guilty by association (era) here, but Fleury couldn't bothered to be hit with one early in games...
Regardless, over enough time, I don't think any goalie's performance would drop because he had a great defense...ancillary stuff like save pct might be affected, but as is well established on this board, I think save pct. can go kick rocks...
As a member of "a different species" you can take this personal experience for what it's worth. I'm a "B-level" (according to standard US adult hockey ratings) beer-leaguer goalie, that converted to hockey after being a higher level soccer goalie. I played only a bit of hockey growing up in Canada (once punched Pronger!), but quit for soccer at a young age.
Most of my experience is as an adult in a draft league, where every 4 months we re-draft the teams. Players are mostly high-school varsity with a very few ex-college/ex-junior A level players. The redrafting of teams let's me play on three teams per year and experiment with different team construction (I'm often the drafting "captain" of my team).
Here is what I've found and chatted with many goalie friends, so there is some truth in here:
1) Getting the puck out (or in at the other blue) matters to your goalie. If you have a chance to get the puck out and don't... I'll stop it for you. But if you keep making the same mistake over and over... it's gonna piss me off, and I can't concentrate when I'm pissed off. I can't help it... and I'm not a pro... but I pride myself on "staying in the game" and all goalies pride themselves on "no mistakes/attention to detail", but if it is obvious to me that you aren't paying attention to detail, a sinister part of me will say "well you deserved it" as a somewhat stoppable shot squeaks in.
2) Trust is built in two directions. I've had solid, stay at home and two-way defenders that were prone to a huge blunder every once in a while. These are the same guys who clear pucks off my line or press them back into/under my pads for a whistle. When these guys blow a tire, I'm more likely to make a save... it's just the way it is. I know they've got my back and my adrenaline will kick in... gotta make a save for Jonesy... must make this save! That adrenaline is like confidence and I'll stay out higher, cut down the angle, never shrink back into the net... and the save will be made if it is anywhere within my physical capability. The same situation with a selfish winger who never passes the puck and turns it over at the blue line? Same thing, I'll stop it for my teammates, and for myself, but he better give me a stick tap. The third time he does it that night? I want to do the same, I want to win, but my brain goes "WTF, not again" and then I don't get that adrenaline rush, I feel frustration, and my SPCT in those situations is lower... no stats... I just know it is.
3) Confidence matters, saves build confidence: To your point... Fleury under siege has just made 3-4 five-bell saves. He KNOWS it's not him. He KNOWS he's helping his teammates. That breeds confidence, action gives adrenaline, games like that are a constant flow of positive energy... until physical exhaustion or frustration with teammates set in. The latter almost NEVER happens in a 2-1 type of game, but if I'm under siege in a 5-4 game where I'm seeing way more action than the other guy, then my hot streak isn't going to last as long... frustration will set in... and then see point #1 and #2 above.
4) Sometimes, playing for strong teams can lower SPCT: but probably not for the reasons you are thinking. On a strong possession team, you will get less shots... and you'll be ready, that's your job. BUT... what also tends to happen on strong possession team is that the shots you DO get are higher quality. Everybody is human and a team of strong defenders will occasionally still give up a breakaway when a pass at the far blue line is intercepted. At the NHL level a breakaway (see shootout stats) is ~50% SPCT.... so obviously that's going to lower your SPCT on that night. Same with a 2 on 1. Same with a team that blocks a tonne of shots, the one that gets through is probably screened, or tipped, or... you see my point. SPCT can go down in these situations, even though the goalie is stopping all of the stoppable shots.
5) But often it works the other direction: A truly strong defending team, one that isn't prone to huge blunders, will improve your SPCT overall. Shooters are pressured on their shots, they won't have time to pick their spot, sticks are tied up, crease area is cleared so I can see, shots then come from the perimeter, etc... all of those fundamental plays shoot my SPCT through the roof. It becomes a super easy night. Ultimately it's attention to details and details are what prevents goals. Goalies live it, defensive minded D-men and centers know it, plenty of forwards and offensive D can be taught.... but one-dimensional wingers... just can't be helped. Never pick (more than one of... and only if you must) those guys