What would happen if I build a half bath without permits?
Non-expert information ahead...  For the most part, nothing happens... immediately.  People do work without permits all the time.  Sometimes its very major work, sometimes it's just a "technicality" and the permit is kinda silly.  Often, no one finds out and no one asks.  I'm not saying it's ok - just saying it happens.

But, since you are planning to sell soon, you really should make sure it's all on the level.  Say the buyer has an inspector come by and he finds any little silly issue with the work.  A good Realtor would ask for the permits on the recent work.  If you don't have them it turns into a huge negotiation tool.  It might not even be an inspector.  Someone could just notice the recent work or see that the number of bathrooms has changed.

Then let's say that you don't sell the house and you live there.  A pipe in the shower springs a leak and you call the insurance company.  Strange - we don't have a record of that extra bathroom.  Where are the permits for the work?  Oh, no permits for this illegal addition?  That's not covered, and furthermore, we are dropping the policy and reporting this to your lender.

Of course cases like that are rare, and that's why people skate by and don't get permits and claim, heck I've never pulled a permit and never had an issue!  Like so many building rules, that's right - you never have an issue at all, until you have a big, huge expensive issue.