Oh yes, it is very possible and indeed done all over now. Most recently I volunteered for a film festival I've worked with for years and the theater they are allowed to host in upgraded to Sony 4K projectors. (these are huge BTW) I had wondered what formats they would use, and then literally saw several store bought Blu-ray players brought in, connected and used for the duration for both DVD and Blu-ray. The image seemed fine with Blu, and as Zombie pointed out, the difference between 1080p and 2K is very very slight.

This has perplexed me as to why people opt for 2K projection. It is really no better than staying at home, where you have a more looked after transfer and audio presentation, plus it costs less and you can have a better experience than in a theater which does not care to present properly.