You can do about anything. Is it safe? Is it wise? Maybe not.
#1). How strong is the gun? Many old .22 rimfires were built around 20K CUP pressures or less. .22 Mag works in the range of 35K CUP. At best, the gun would "work lose." At worst, it would blow in your face and if you are lucky, you DIE!. [WHITE CANE time...] Today's versions of the same model are newer steel or better heat treat or
and safe that way.
#2). .22 Long Rifle uses a lead bullet at .222. .22 Rimfire Mag uses a .224 bullet. Is this going to blow the gun up. Probably not. Will it improve accuracy. Probably not.
#3). Cost. A cheap, quick rechamber might go $50.00 unless you have a friend... Maybe more. Top flite work, a lot more. A new gun would be about twice that. A used gun? Shop around.
Can you. YES. Should you? Probably not. LUCK.