Can you have braces if you've had fissure sealants put on your teeth?

Absolutely. In fact, the sealants to protect those back teeth may be seen as an advantage. Often orthodontists are placing sealant materials on the front surfaces of other teeth to protect them as well during braces treatments, too.
Braces. Yes, you can. In fact sealants are recommended with braces but are not required.
Absolutely. Yes, in fact it's a great idea to have sealants when you have braces, because the orthodontic hardware has a tendency to collect more debris and food particles which can lead to decay. While sealants don't make your teeth immune to decay, that sure make it harder to get cavities. Good investment!