Can I put Transcript sidecar Files next to proxies rather than the raw media?

I'm not sure which files you mean by transcript sidecar files. Are these .prmi or .json files?
 

Neither one will really work as a sidecar file for the transcript. The .prmi file is just a cache of what Premiere Pro's media analyzers produce, so the media doesn't have to be re-analyzed when it's reused. The transcript itself is always stored in the project file.

The .json format does let you bring a transcript into Premiere Pro with word-level timecodes intact, but it attaches per clip. Even if you send your editors a .json file for each transcript, they will need to attach each one manually.

More importantly, if you're using a proxy workflow and want the smoothest online conform down the track, I recommend creating a project file with the raw media linked and the transcriptions included, then sending it to your editors on a drive along with the proxies. This ensures the metadata and the resolution of the original footage are stored in the project, even though the original media is offline.
 

More detail on both formats here:

How to update .prmi sidecar files

Now in Beta: Import Your Own Transcript