That setup will be fine with the 550. At max load, you should be pulling ~475w at 4.7ghz using 1.6vcore. The 7870 will pull ~130w at stock load and maybe 170w with o/c. Stock 7870 plus 4.7 o/c will need about 31 amps on the 12v or 35-38 amps with gpu o/c. The seasonic has 45amps on the 12v rail.
You should be good to go.