My baby is 5 weeks old. My wife likes to breastfeed and then let him fall asleep on her breast, anywhere from 20 - 30 minutes after.
Would he get used to falling asleep on the breast? To the point where he won't want to sleep by himself in the crib? Lately, I've been having trouble putting him down to sleep, but I can't tell if he's just struggling like a regular baby, or if it's because he's gotten used to falling asleep on breast.
Falling to sleep while feeding is a completely natural thing for a small baby. In general young babies don't want to sleep anywhere by themselves. You are in the "fourth trimester" e.g. see this information where baby is getting used to being outside of the warm, snuggly womb and they like to be cuddled up to their parents. Sleeping in a big, flat, cold crib is what baby has to get used to. You could try making sure baby is all wrapped up with some sort of sleep-safe swaddle (only until they can roll over), making sure the sleep surface is pre-warmed (we used to put a hot water bottle in and remove it when we put baby down) or babywear for naps so mum can do things. We also researched safer co-sleeping guidance from a UK safe sleep charity as it is much safer than accidentally falling asleep on the sofa when you're trying not to, and allowed us to all get a much better night of sleep.
Over time baby sleep is very much non linear. You'll think you've got it and bam, they won't sleep for a couple of weeks and they'll go back to normal! You'll find yourself regularly wondering whats gone wrong over the next two years.
Yes, your baby can become so accustomed to this that it will be harder for them to fall asleep any other way...but those sleep associations don't start to form until about 3-4 months. So don't worry about establishing undesirable habits yet.
But as the other poster says, bedsharing is not as safe as getting baby into their own space. So don't fall asleep yourself if baby isn't in a safe sleeping space.