You still need people to pilot the things (though of course they are sat at a base somewhere) and service them, i don't see how it can help the manpower problems.
Far, far fewer crew needed than for manned aircraft.
Servicing of something like Mantis should take far fewer crew than a manned aircraft. It's smaller, lighter, simpler. Even Taranis should be much easier to maintain than anything manned.
Operating them is also less manpower-intensive. Unlike the USAF, the RAF doesn't have hangups about only fully qualified pilots being able to operate their drones, or insist on them being "flown" all the way. IIRC, Mantis or Taranis are supposed to be capable of being operated part-time, flying themselves most of the time, with operators monitoring, & only intervening occasionally (e.g. saying "take off now", "fly to coordinate X", "fly search pattern Y", or "fly home now"). You should, in theory, be able to have one operator (probably an NCO technician, not an ossifer pilot) running two or three of 'em while a reserve or two has a nap or a cup of tea, ready to step in if needed.