No. The slang word 'stroppy' comes from a shortened version of the word obstropulous, or obstreperous. It means to be 'uncontrollably noisy', yet we use it as being more like 'moody' or 'bad-tempered'.

The word 'strop', on the other hand, has two completely different meanings.

1. A piece of leather used for sharpening a blade.
2. A bad mood.

'She's got a strop on' = 'she's in a bad mood'