Is this NPN transistor AND logic gate practical?
It does work as an AND gate, but there is no gain for input B -- so you can't use its output to drive another gate's Input B. 

For a logic family to work well, you need to have the output signal go high and low, and also be able to drive a number (fan out) of similar gates. 

You could make a gate with input A and the V+ input of Q1 -- it would generate 
OUT = A &amp; not(B). 

That gate would have gain.