Two NPN Transistors in C-E to C-E Series?
So the question is, can I put two NPN transistors in series, C-E to C-E, to function like an AND gate? If not, Why not? Will it damage anything?


Theoretically you can, but this will result in: 


an increased VBE of the first transistor (increased by VCE of the new transistor); this may cause the transistor to dip into the ohmic region, and you may need to change R1 in order to compensate.
possibly reduced ICE if the current is limited by a simple resistor instead of an active current limiter; this could result in reduced maximum brightness.


Fortunately these can be tested by placing a couple of diodes after the existing emitter.


  If my added transistor is off, will there be any negative effect on the first transistor being pulsed?


Hard to say. If the existing circuit uses a resistor for current sensing then it may "overdrive" the PWM in order to compensate for the now non-existent current. This may become an issue when the new transistor is turned back on.