The power output of a TC'd aircraft will increase with altitude -for example the seneca II is rated at 200hP at SL but at altitude 215HP which is why one can officially do an FAA High performance endorsement in it.
As mentioned there ae two sorts of turbo aircraft - Turbo normalized aeroplanes, like the T182T which maintain sea level MP up to altitude by varying the amount of pressure the waste-gate dumps. These can be flown like any other normally aspirated aeroplane and the throttle can be firewalled on take off and at low altitude would perform the same.
Then you have turbocharged aeroplanes, like the Rockwell Commander and Seneca II. These actually generate more than atmospheric manifold pressure at sea level, which means if you firewall the throttle on the runway you run a serious risk of over-boosting the engine. Normal take off in a Seneca II uses 39" of MP, and the commander can use up to 42" MP. I assume this increases performance even at low altitude. They do have wastegate valves to dump excess pressure if accidentally over-boosted but it depends on the speed of operation as to whether the engine will suffer any damage or not.
The DA42 actually uses over 60" of manifold pressure - not that you care because the FADEC takes care of it....