Many years ago, when I was first getting involved with PICs ( not PICaxes ), I had a board from a company called, I think, Magenta. It had a pre-programmed PIC on it, the IO of which was driven by a serial line from a PC. You programmed on the PC in PIC assembler, which then ran on a simulated PIC engine, which then used the IO of the real PIC to drive real world stuff.
It was clumsy, buggy, and slow, and I never really used it much. The Microchip IDE was much easier to use, and very soon PICs had the in-circuit debugger facility which made this kind of tool redundant.
Today, with the higher speeds and bigger codespace, I reckon a PICaxe running some PICaxe BASIC code could easily do the same job as the Magenta.
So pressing the 'Simulate->Connect' button would download the IO driver code, and the PE simulator would then talk to the IO.
It doesn't sound like rocket science, the PE simulator already does all the hard work, and writing a bit of code to drive the IO would not be too difficult.
I know it wouldn't cope with the functions that depend on soft timings, but even stuff like AtoD, I2C, and HSerial should not be too difficult as the PIC hardware and PICaxe firmware does all the critical work.
A facility like 'Simulate->Connect' would make educational systems more 'visible', would make debugging hardware a lot easier, and would be useful tool for beginners.