Odd question - is it possible to collect / buy all the pieces to assemble a mech or do you need one that's already been built though has potentially been gutted?
What you're describing is a hole in the rules since they started doing Mech prices. It's cheaper to buy all the components of a Mech and assemble them into a functional unit than it is to buy the actual Mech. It always has been. There's a flat +% cost modifier (or something similar) applied at the end of all Mech construction. It's a known issue, and it's something which can't be fixed without going back and retconning a ton of Mech prices, and CGL doesn't want to do that.
I would rule one of two ways, and honestly, I don't have a preference:
1) No, you can't build a Mech to take advantage of the rules loophole (even though that was not your intention).
2) Yes, you can, but you'll have to pay the difference in C-bills (miscellaneous costs related to the process of constructing a Mech without an actual factory).
IMO, the easier route is to simply require that you have the CT of an existing Mech with 1 IS point left in it, and you can buy everything else and rebuild it from that 1 remaining IS point. But that does require you to have the CT available in the first place.