Unknown_K is pretty much spot on. The great Amiga/PC struggle can be compared to the tortoise and the hare. The Amiga bolted off ahead, then paused for years whilst the PC tortoise slowly but surely passed it by - getting faster with each step.
The A500+, A600, and CDTV were complete wastes of time and resources (for me the CD32 killed off the Amiga). They were not a step forward from the A500/A1000 in all honesty were they?
One should always compare the equivalent Mac Hardware to see what Amigas *should* have had at any stage post 1987.
As Unknown_K said, Commodore should have adapted a two stroke strategy; one games machine line to stay ahead of the consoles and another business machine line to stay ahead of the Mac and Pcs in the multimedia field (as the business market was by then sown up):
Releasing the A1200 in 1990/1991 would definitely have been the best bet. It should have been an AGA spec 030/040 based machine around a built in CD drive (to get round pirating as cd burners were few at the time) with an external disk drive and external SCSI port for harddrives etc. That way it would have stayed ahead of the SNES and Megadrive, which was the bare minimum if you ask me.
And all this whilst pushing forward the high end A3000, A4000 as Mac/PC killing multimedia machines.
But to answer Jherek Carnelia original question, i dont think the Amiga could have gone on to become the ubiquitous machine that the PC is.
The Amiga dawned in 1985, the PC was already established in the business world by then. With Commodore's useless excuse for marketing personnel, they didnt have a chance in hell to alter that. But it could have survived as niche platform, you see in all honesty, one has to say that if Apple has survived, then so should have the Amiga.