It depends on your card issuer.
With American Express (UK), I've had no problems overpaying, then putting through a charge for positive balance + most of credit limit. I actually rang them up to ask the first time I wanted to do this, and they confirmed it was fine, but warned me that their website would only report an "available credit" of the credit limit, not including the positive balance too.
On another card, I normally round up my monthly payment, so at the start of the month I'm normally a few pounds in credit. When I log into the online service for that card, it shows the credit limit as normal, and an available credit of credit limit + positive balance. However, when I asked the card issuer about putting a noticeable amount of overpayment onto the card for a big purchase, they said that it wasn't allowed and they'd reserve the right to close my card down if it I did it, and it wasn't something they normally allowed.
So, I think you best bet is to ring your card issuer up and ask them. If they give you the nod, overpay a few pounds/dollars/euros/etc, then check your available balance & credit. If it hasn't gone up, ring to check, then when that's sorted make the large overpayment and finally use the card!