Yes but those sessions can all share a single source port, assuming they are all to different destination IPs/ports. (TCP session identity is determined by both the source and destination ports and IPs.)

IIRC most web browsers do not open more than 2-4 simultaneous connections to a given server. So an allocation of ports an order of magnitude larger than that should suffice for a typical home user.

(Not that I'm advocating such crazy NATing!)