You need to be able to accept incoming connections to be able to fully participate in the network. Last time I seriously looked into this, BitTorrent clients didn't support any sort of NAT hole punching (and they often work over TCP in any case). Try running a client with and without a forwarded port and you will see massive difference in the number of peer connections.
Transmission has supported UPnP and NAT-PMP for many years. Although it doesn't always work as reliably as having a client with directly routable address(es), it does exist and works okay.
Of course, but if everyone is behind the NAT then no one in the swarm can connect to any one. If this is a popular torrent when someone with the connectivity would show up, eventually, but otherwise good luck. Recently it took me four months to complete one torrent and I was the one with the real IP.