Not that I am aware, I've got my mail server set up and its using 80 and 443 right now, never had to ask them to open them up... 

no.

if port 80 and 443 are blocked you would have no internet

biggal:

 

if port 80 and 443 are blocked you would have no internet

 

The OP means blocks on incoming connections on ports 80 and 443, where he might want to run his own web server.  Outbound connections to 80 and 443 will have their inbound port number >= 1024 and would not be affected by such blocks, so access to outside web sites would work fine.