Well, maybe. You asked about fps (frames per second), which is NOT linked directly to resolution. The display device is one thing that can limit fps. Almost all recent high-resolution devices will do 60 Hz screen refresh rate, but some can do 120 Hz or higher. So, IF, for example, your monitor can do 120 Hz, and your TV can do only 60, AND your actual frame rate has been better than 60 on the monitor, then the TV may slow you down a little. BUT if your actual fps rate is no more than 60, OR if your TV can do higher refresh rates that that, you will NOT experience any slow-down.
NOTE that, if your system does not have a custom video driver for your TV, you may have to use a generic driver and adjust its parameters to match the TV's in...