If you google "kauffman material imbalances" you'll likely find a very informative artice writtem by then IM Larry Kauffman which address questions like yours. Or it may be on this site somewhere. I believe the following paraphrases it though.
These are my opinions based oin my recollection of the article. Take it easy on me all you chess experts ;)
I think the 'bishop pair' is a material rather than positional item. As such, I would consider these points:
1. Giving up the bishop pair leaves MATERIAL imbalanced (depending on the number of pawns on the board the bishop pair could be worth anywhere from -1 to +1 to your opponent.
2. Positional considerations (like doubled pawns) usually come into consideration only when material factors are even. In other words, you would never take pride in giving up a piece to inflict an isolated pawn on the opponent. In that case, the isolated pawn 'defect' is irrellevant.
3. As to whether the material imabalance can be 'masked' in the tactial heat of a game, that is more likely to occur with major pieces still on the board. For example it is much more acceptable to sacrifice the exchange with queens and rooks still on the board. Sacrificing the exchange with only minor pieces left on the board is harder to understand. Granted the bishop pair is not as glaring a material imbalance as the exchange, but it is material none the less.
4. The bishop pair is permanant, whereas your opponent may be able to fix some or all of his isolated pawns.
Is it considered sound compensation to trade both bishops for both knights to gain two sets of doubled pawns? It seems a bit daunting to face the bishop pair with two knights.
If the queens are off the board, does the above favor the bishop pair's side even more.
Been grappling with this question lately, thanks for the input.