They may, but they definitely wouldn't be anywhere NEAR as willing to use the right as godaddy, if ever.
Out of the 30 domains I have at NameCheap, I've lost 4 of them due to NameCheap deciding that certain domains shouldn't be related to certain topics.
Of the similar domains I have currently at GoDaddy, they have taken away none.
I had a friend just get their domain back after NameCheap decided to do this shit. It was a .CA, and they got CIRA involved. CIRA agreed that NameCheap fucked over my friend, and now the domain is at another registrar.