No. If you don't convert your Bitcoins to hard cash, you don't need to pay any tax on it. As long as your investment remains in the form of Bitcoins, the government can't tax you. If you sell your coins within three years from the purchase, then you need to pay regular income tax over it. If your investment is over three years old, then you may only need to pay the long-term capital gains tax.
If you are country is being too strict on implementing tax laws then you would definitely pay up taxes when you are already converting your bitcoin to local fiat but actually you can evade tax if you do want too which you should only cashout on minimal amounts gradually not on bulks so that it wont really caught their attention.For now you shouldnt still bother or stress out yourself regarding on this as long your investment is on bitcoin form.