In the good old day's when the modern tent was made of canvas, it was vital that you never packed it away slightly damp, as the inevitable condensation build up would destroy the fabric in no time at all.
I can remember many years ago, staying with a friend in West Wales.
A tent he had stored away in a cupboard in his garage, was full of mildew and the brass studs used to fasten the storm flaps had worked their way lose from the tent itself.
The tent was not old, so poor maintenance and storage meant a perfectly good tent was almost next to useless.
Most tents today are made from synthetic materials, so its still important to ensure their as dry as possible before you store them away, but the damp will not effect them as much as canvas.
A tent it an expensive purchase, so however inconvenient it may be to dry it before storage, it will ensure it will last many years.
Try not to force dry it in a hot room, like many walkers ive seen do with their leather boots.
The best solution really is to dry it off outside, when the weather will allow, but if your unlucky to be using it on one of those typical wet holidays', make sure the fabric is free from dirt, and dry it off as soon as possible.