Is '我还需要多加练习' okay as a dance video caption?
我还需要多练习 (I still need to practice more) already expressed what you wanted to say, but the statement seem plain, and in a matter of fact tone.

我还需要多加练习 (I still need to increase practice more) .  emphasize the keenness in your intention.

'加' in '我需要多加' (+ verb without object), just like your caption, is short for '增加' (increase) 

If there was an object, then '加' would be short for '施加'  or '加以' (apply to), for example,  对你的孩子多加管教 (apply more discipline to your child) 


  is 我还需要多加练习 a natural way of saying this or would I need change it?


It is very natural, nothing wrong at all.