I've looked at the five teams Roy played on that reached the Stanley Cup finals.
Offense
Season | RS GF | RS GA | Change
1986 | 4.13 | 2.8 | -32.1%
1989 | 3.94 | 3.19 | -19.0%
1993 | 3.88 | 3.3 | -15.0%
1996 | 3.98 | 3.64 | -8.5%
2001 | 3.29 | 3 | -8.9%
Average | 3.84 | 3.19 | -17.1%
Roy's team scored significantly less in the playoffs. On average, they scored 17% fewer goals per game in the playoffs, compared to the regular season. In general, teams score less in the playoffs, but it's roughly a 10% drop (if someone has the exact numbers for those seasons, please let me know). Thus, Roy's team scored even less than we would expect, even taking the general drop in offense into account.
Shots allowed
Season|RS SA|PO SA|Change
1986 | 26.8 | 24.9 | -6.8%
1989 | 26.3 | 26.3 | -0.3%
1993 | 29.8 | 30 | 0.8%
1996 | 28.5 | 26.8 | -6.2%
2001 | 24.7 | 25.7 | 4.0%
Average | 27.2 | 26.7 | -1.8%
This table compares shots allowed per minute in the regular season and playoffs, multiplied by sixty. On average, Roy's teams tightened up somewhat in the playoffs, preventing an extra 0.5 shots for every 60 minutes.
Roy's save percentage
Season|RS Sv%|PO Sv%|Change
1986 | 87.5% | 92.3% | 4.8%
1989 | 90.8% | 92.0% | 1.2%
1993 | 89.4% | 92.9% | 3.5%
1996 | 90.8% | 92.1% | 1.3%
2001 | 91.3% | 93.4% | 2.1%
Average | 90.0% | 92.5% | 2.6%
In each of the five times that Roys' teams advanced to the Stanley Cup finals, he played significantly better in the playoffs, compared to the regular season.
Summary
When Roy's teams advanced to the Stanley Cup finals, they were clearly weaker offensively (compared to the regular season) while being virtually unchanged defensively. On the other hand, Roy played significantly better in the postseason each time. This (along with the fact that he holds three Conn Smythe trophies) provides evidence that Roy was an essential part of his teams' playoff success.