Flight Service uses a different set of radios and can relay messages to ATC, but they've been slowly dismantled over the last two decades and wouldn't have the capacity to step in for an outage (nor should they be expected to - that's not their purpose).
Some aircraft have CPDLC for text-based communication, but it's asynchronous and you can't use that as a replacement for voice communication in the terminal environment. Also, many aircraft aren't equipped to receive it.
Pilots are trained on lost comms procedures, so if you're in the air and the radio fails they'd fall back to those regulations. Basically all the aircraft would fly their last assigned clearance, and attempt to deconflict manually with other aircraft over air-to-air radio (similar to flying into an untowered airport).
There are contingencies for radio outages, but yeah, everything going down at once (if that's what's happening here, which I doubt) is bad.
So it falls back to local control, more in the style of visual flight rules. Pilots in existing flights will have to be vigilant and do their own deconflictation and new flights are banned out until the network is back up.
All conjecture at this stage of course, but all the radios won't just fail. It is probably going to be a poster child example about the dangers of large scale integration. The attraction of course is that integration is very efficient, the danger is it tends to fail all at once instead of in smaller pieces.
VFR traffic doesn't necessarily need radio, and is not affected by this groundstop.
As for lack of radio, this would only work if ATC blocked out your entire route from start to finish - which isn't practically ever done. Otherwise, they need to be able to maintain positive control over your flight since the airspace isn't reserved, which means conflicts are possible.
If you lose radio communication, it's an emergency and they'll move everyone out of your way. This doesn't work very well if everyone loses radio communication simultaneously.
Could you in an emergency, if you had no other options? Yes. But ATC can't legally give you a clearance that was dependent on using ADS-B for separation.
(Similarly, if there's a potential traffic conflict, and you tell ATC you see the other traffic on your ADS-B display, they just have to disregard that statement and assume that you can't see the other aircraft at all.)
I would hope that airports keep a battery operated radio + antenna in case of emergency with them, to at least communicate with aircraft within visual range of the airport.