i would leave it till it does maybe but yes there is a very good chance and it may take a while.i had about 5 new plants but 3 were week so i have 2 good ones now.

how long will the new shoots take to come through.

could be up to 6 months mate but its still worth it.i guess you could cut the old plant back a bit just to tidy it up a bit.

If there's no sign of growth from the centre of the plant by beginning of May, cut it down, checking for signs of babies near the base.