WTF makes you think your boyfriend thinks normal length eyelashes are ugly? Here's a tip. Guys don't give a rat's ass about your eyelashes, eyebrows, hair length, hair color, moisturized skin, and pretty much everything else you worry about.
But to answer your question, it's a bad idea to sleep in eyelash extensions.
I'm pretty sure you would wake up with one on your forehead and the other on his pillow, and he would be much more worried about the weird objects he found in his bed then you minus eyelash extensions.
I might leave a little eyeliner to bed, but worrying about looking ugly in your sleep? He doesn't care. In the morning it would look all weird anyway. Best go natural.
I wouldn't wear any form of makeup or anything on my eyes when I sleep. Eyelashes won't make that much of a difference. If you feel you look decent with eyelash extensions then you look decent without them too. If your boyfriend thinks you look ugly because you don't have your lashes on then you have bigger problems. Don't worry about it!