may or may not - if it's ring wired the two cables come from either side of the ring (leading to and from the prev socket)
most lectricians are to say the least economical with cable - so slack isn't always available
unless you are comfortable with a bolster - measure the depth ... wrap tape round a masonary bit ... and drill the wall a few times to make it easier to cut when the banging (obviously if it's a partition wall - cut with a good stanley knife - but not the wooden support)
the box should be 1/4 inch below the surface of the plaster
you'll be filling the old hole so slap a bit behind the box - push it down so it sits firmly - then fill the rest of the hole and it will hold ok
additionally if you feel better
no more nails will make a semi permanent job (you'll never get it out!!)
or drill and fix with a couple of short screws - but don't go through the wall