[judgmentday]

Should I use any existing amplifier as a headphone amplifier?
Yes but with caution.
1-) Do all the connections while the amp is off (disconnect it from the electric outlet)
2-) Lower the volume of your source to the minimum
3-) Lower the volume on your amp to the minimum
4-) Turn on the amp and increase the volume just a little bit and listen to the headphones without putting them on your head just to hear if the volume is ok.
 
I have tried this with Audio Technica ATH-ES7 and HD650.  They sound great.

I have a great amplifier, and it would seem a waste for me just to sell it.
Sure. You can use it as a great Headphone Amp.

Is it possible to add a headphone output to the amp and make it into a headphone amp or is more involved?
No need for this, just connect 4 wires directly to the amplifier speakers terminals and wire a 1/4 female Stereo headphone with 3 contacts: tip, ring and sleeve (Left, Right & ground).
 

 
 

1/4 Female Stereo Headphone Jack with 3 contacts (Left channel, Right Channel and Ground)
 
Is it worth it? Am I better off getting a dedicated headphone amp?
Just try first how your existing amp sounds; if you like it you don't need a new headphone amplifier.

 

[bighat]

is not dangerous to connect headphones to t-amp?

 

[jcx]

some Class D, switching amps only have bridged outputs so tying R, L Black together is a no-no since both are active outputs, not common ground
 
some tube amps with output transformers are reputed to be able to damage themselves without low enough resistive load on the output winding
 
 
 
a resistor divider on the output can match the gain better for the headphones

 

[bighat]

here is a post about t-amos and headphones
http://www.head-fi.org/t/618443/why-cant-a-t-amp-drive-headphones#post_8531747