Yes... Depending on the size of the carboy, you might want to get a blow-off tube setup so that you're ready if fermentation goes ape-nuts... OR get some fermcap (about $2) and add that post boil to keep the krausen down... Either option will work, and the fermcap can also be used to keep boil-overs to a minimum (even if you have very little head space in your brew pot)...
I've only used the bucket primary that came in my kit for two batches. Everything else has been in either my 6 gallon carboy, 5 gallon carboys, or my 5 gallon keg(s)...
As long as you compensate for the reduced head-space in the primary, you'll be fine... I would just not use a really top cropping yeast in a 5 gallon primary (for 5 gallon batches, 4 gallons of wort should be fine though)...
I'm shifting over to using kegs for primaries now... I have one 5 gallon corny and four 5.16 gallon Sanke's... I plan to use 2-3 of the Sanke's as primaries, and the other(s) for aging bigger brews...