Converting movie files

Yes you can, but it won’t improve quality, as the source will likely have 4:2:0 chroma and a lower bitrate.

You will need other tools than QuickTime Player to do this conversion. FCP should be able to convert on import, as it uses it as its intermediate codec.

You can also do these in batches with Compressor.app - given the price difference and configuration options, this would be the preferred method.