If we compare it to the WoTLK alpha two years ago, they patched the client like 4 times before going to closed beta, being the Beta client itself the 5th patch that introduced the WoTLK login screen. It lasted for two monts, going from May to early July of F&F Alpha then another 5 months of Closed Beta.
If Cataclysm F&F Alpha is going to be as long as WoTLK's, and given how far they progressed in it's development just for an Alpha, then we'll see at least two patches before going into beta.