I don't know about the E1000 (PSP Street), but the other models including the go definately allow full hacking with just the stock system, and a memory card, or internal memory with a PSP Go.
The hack is just copying the files to the memory card/internal memory and then running the program that appears just like a normal PSP game. If you don't have a cold boot CFW, to rehack after completely powering down/rebooting just involves running the reloader which also appears as a game, which takes all of five seconds and is self contained and doesn't networking access or anything else.
There might be some really old homebrew that needs 1.5 to run, but I'd wager anything you want to do can with done with the latest CFW. So cold booting CFW is really the only difference. And while I don't always play on my PSP, when I do it's on my Go.