You will NOT get better accuracy with a free-floated barrel.....and the standard plastic stock. Probably the opposite, in fact. The stock is simply NOT rigid enough. That is why the stock comes with pressure pads to contact the barrel at the front of the forend. You could go to the trouble of reinforcing the forend of the stock, to make it more stiff (I have done this on the ADL's), but free-floating still MAY not improve things. The plastic stock is not rigid enough even in the receiver area, which is CRITICAL if free-floating is to work. You MUST glass-bed the receiver area, if free-floating - otherwise, it is a waste of time. It is difficult to glass-bed the injection molded plastic stocks. I have done it.....and successfully.... but it ain't easy.
If you really want to free float the barrel, you'd likely be better off changing to a stiffer stock - wood, fibreglass, or laminated wood (the stiffest of all). Even then, it is still necessary to bed the receiver, or free-floating may just introduce MORE movement into the system (which will HURT accuracy).
If the standard plastic stock is warped and some portion of the barrel channel is touching the barrel (other than the pressure pads), then yes, DO address this. But, I'd recommend NOT messing with free-floating - unless you plan on making a proper job of it.
Free-floating is one of those concepts that everyone thinks is the be-all and end-all of rifle accuracy - and that is NOT the case. That is a MYTH. Free-floating will improve things with some rifles - but NOT ALL of them. The fundamentals have to be right FIRST (rigid stock, bedded receiver). Even then, with a sporter-weight barrel, FF MAY not make any improvement. My old Mauser, with a mid to heavy weight barrel (not a bull barrel, but heavier than a sporter barrel), short and stiff (17.5") and a rigid, cross-bolted stock with the receiver carefully glass-bedded, STILL is MORE accurate with barrel pressure pads in the forend.