Yes or No. A very complicated question! Yes means, I guess, if you transfer TFSA to another financial institution, your TFSA capital growth will go with it . There would be no tax implication. However. If you withdraw all of it from your TFSA, including your capital growth, and you want to put them all back into your TSFA in next year, the amount within your contribution room will be no problem for sure. But for the growth portion, not sure. You can call CRA to find out. As I understand, it's probably not allowed. I knew someone called CRA regarding the same issue you asked, CRA could not give a clear answer, just said: follow the TFSA contribution formula.
The TFSA contribution limit, 2009: $5000; 2010: $5000; 2011:$5000; 2012: $5000; 2013:$5500. For instance, you have used all your contribution room, and you are going to withdraw all the money from your TFSA now. You have $27,000 in your TFSA ($25,500 you put in and $1,500 capital growth). In 2014, you can put $25,500 +$5500 (room for 2014) back in your TFSA. As for $1500 the capital growth from your previous TFSA, no one sure. It's your call.
This is only my 2 cents. There are a lot of big CFCers who may give you better insight.