Yes it will affect accuracy, and quite badly too if it is loose enough.
I had that problem at the last THL meet where mine came loose during the HFT comp, so I was compensating for distance, wind and the loose barrel......not good!!
The Remedy...
Take the cylinder off and have a look on the face of the block, you will see an allen head screw in a recess
Tighten this up and you should be fine
I had an extra one at the top added on mine by A & M (theyre not far from you!!) just to aid security, no more problems!
Darryl