They should have been aware. They had multiple vulnerabilities beginning with cap space. They have an experienced super agent running the organization who's leveraged the CBA for client value including recent team negotiation with the Connor Brown contract. If the Oilers suspected the players were not going to sign 'fair deals' (team budget vs. market), then even more they should have moved early and aggressively to move the players. It was public knowledge St. Louis discussed both players at the deadline and by some suggestion the trade deadline two years ago. The Oilers were in the market for veteran players for the past several seasons and among their prospective trade assets were Broberg and Holloway.
I could easily argue that unless they were explicitly told that there was an OS in play that there was no reason to increase their offers or to move either player. The vast majority of these situations, probably 95%+, resolve themselves in the team's favour. But if they were made aware of the threat of an offer sheet, or even strongly suspected it, trading the players would have been more challenging.
While not quite the same of course, we have recently seen some very good players let go because of the threat of pending arbitration, and not just by cap-strapped teams. Teams are always reluctant to give RFA's too much because of the significant inflationary impact such deals have and those that are in a position to sign for more than the norm have seen their value decrease substantially. Neither player was arbitration eligible, but any significant known or even perceived threat of an OS would have had a similar dampening effect. It seems clear that any team looking to acquire these guys would have similar knowledge of the situation. Aside from St. Louis the threat of a significant OS would have been an issue for any team looking to deal for the pair or individually, reducing the compensation.
From a risk management point of view I still do not see any significant error that management made. They did not lose the players for nothing, nor were they ever at any risk of doing so. At best the compensation that they might have received would very likely have been only a modest improvement on what they got. That is just a historical fact. Frankly, as much as I am disappointed that they lost both players, because of the extreme value of cap space to this team, I actually think that at least for the next two years the team is currently in a stronger position to succeed than they would have been had they given them much more than they were offered.