In this situation can the glider pilot actually use the radio to request landing permission?
Full Sutton is an uncontrolled field with A/G service only. A/G cannot give landing permission, only airfield information like circuit direction and runway in use.
However, my flight guide has this to say about Full Sutton: "PPR. Non-radio ACFT not accepted. Radio use is mandatory." and "Intensive gliding at Pocklington, 4nm SE of AD."
Assuming that he did not have a radio licence.
From personal experience I can testify that glider pilots, at least initially, seem to fear the radio like the plague. During my weeks long glider course my instructor did not use the radio once. In fact, I don't think we even had a mike on board.
There's a few glider frequencies that are exempt from the requirement of holding a radio license. A typical A/G frequency would not be exempt so yes, you need a radio license, but that's something that's only acquired rather late in your glider flying career. Not, like in powered flying, together with your PPL.
So the glider pilot may or may not have had a radio license. Nevertheless, if the situation was developing as rapidly as some have suggested earlier (poor situational awareness combined with a high sink rate due to wave), even with a radio license, he might not have time to figure out what airfield he was at, look up the frequency, select it and make the call. My flight guide also doesn't show a signals square at Full Sutton so without a radio it would be impossible to know the circuit direction and runway in use. Unless you spot and follow circuit traffic, of course.
But even if he were to know the circuit direction and flew a neat pattern, conforming with the other traffic, it would have been bad form to land *on* the runway. After all, gliders can't taxi clear but need to be pulled/pushed clear. When you land at a field which doesn't normally receive gliders, and also doesn't have a fire crew standby, it may take several minutes before people realize what is happening and a group of two-three people has been assembled to push the glider clear of the runway.
I'd guess that the tower would not be monitoring the gliding frequencies?
As said, we're not talking about a "tower" here, but an A/G frequency, which would be addressed as "Full Sutton Radio" - despite the fact that they are probably sitting in an air-traffic-control-tower-like-structure. But yes, you can bet they won't be monitoring the gliding frequencies - after all there are no gliding activities supposed to take place at Full Sutton.
The only thing that theoretically could have happened is that he would broadcast his intention to land at Full Sutton on the Pocklington Glider Ops frequency, and that somebody at Pocklington would give Full Sutton a phonecall to warn them of a glider dropping in unannounced. Full Sutton would then be able to warn the aircraft in the circuit. Lots of if's in that scenario though.