I am finding conflicting information. On one hand..
As I understand it, newer Singstar titles on the PS3 (SSp3) shipped with two separate usb mics instead of the adapter, likely the reason why these titles also accept third party or alternate usb mics. Instead of the 2 separate mics on one usb, it is now 1 analog signal per usb input, which is how most of the other software interpreted the input. The adapter may have made the SS mics usable on such software as well, though perhaps at reduced performance, or perhaps only in single player mode since the other software isn't prepared to look for the player 2 input on the same usb channel, and conversely why the SSp2 titles couldn't use other mics which DIDN"T carry the second channel at all in the usb1 input.
That would also make the most sense; USB mics are all extremely standard and this would maximize compatibility and thus sales.
On the other hand..
Singstar 2 arrived today and I tried it with my two Logitech USB mics.
It doesn't work. :( These mics work in the PS3 audio-in setup, but within Singstar it says there is no mic. It looks like I could get 'jackplug type' mics working on it if I had a Singstar USB converter. Anyway, just thought I'd point it out here in case anyone else is trying that route. From what I've read elsewhere it seems some USB mics do work, but not the Logitech mic that came with High School Musical for the Wii and not the other Logitech USB mic I have.
Sony is also the company who invented the glorious proprietary Memory Stick format (now dead, thankfully).
So, I would file this under "try at your own risk.."