sounds kinda similar to what I do, I use a cooler (unconverted) to mash in. Then I transfer the mash to a 5 gallon bucket w/ a plastic spigot and a nylon paint straining bag to lauter and sparge. Works fine for me.
The only reason for the cooler is to hold the mash temp steady. I've been able to hold the mash for a full 90 minutes without losing even 1 degree F. So, unless you have trouble holding the mash temp, I don't see any problem. If you do have problems with your mash temps, a cooler costs about 15-20 bucks, so it may be worth it.