No, 23andme specifically bars anyone but the person whose DNA it is...from submitting. However, if they have a fairly complete sequencing of the DNA, I don't think GEDMatch does.
GEDMatch will almost certain lead to some distant relatives - who might also be in 23andme (because GEDMatch itself doesn't sequence DNA - most people come in with DNA sequenced by Ancestry or 23andme).
23andme uses only its own proprietary saliva sampling kit - not blood, not ever (not set up for it).
Once run through GEDMatch, LE can probably find relatives which may be enough for genealogical research. As that researh progresses, its quite common for distant relatives to be asked to get their DNA sequenced - to get closer and closer to the perp.
23andme would argue strongly in court that someone violating terms of service (in your example, LE) are not entitled to any results. Every person submits for themselves and signs the ToS (which includes info that if compelled in court by warrant or subpoena, 23 will give up your DNA - but not necessarily one's ancestors).
LE could also ask someone who is a relative of a suspect to submit to 23andme, voluntarily share all their results, etc. I would share and don't really understand why someone would not. Of course, I don't have many bio-relatives, most are already dead, and I'm pretty sure neither my kids or grandkids have committed major crimes.