I've had posters removed from foamcore before. It's possible, but it can be very damaging to the front of the poster depending on what kind of glue was used (unfortunately it seems they never used wheat paste or a water-based glue, then it would lift right off). Think of it this way... you aren't dissolving the glue so much as you are scraping the poster off the board. The restorers get the poster wet and just start chiseling at it. It's crazy time consuming and it is almost guaranteed that you'll tear through to the front of the artwork on multiple occasions.
So again, it's A) possible, B) expensive, and C) potentially damaging -- but for the right poster at a low price, I would and have done it.