Not really. I would have to be the proper owner of content they posted that clearly violates DMCA.
I'm not about to go and break the law by abusing DMCA takedowns back at them, as they likely just did to me.
They have expensive lawyers, you don't
If they go after you for the same thing they themselves did aren't they just handing you the means to go after them?
They're not paying for your lawyers. It's that simple. Unless you have a deep war chest any competent lawyer would tell you not to pursue it.
Microsoft has expensive lawyers on retainer, and would not challenge the takedown notice against youtube-dl.
Those lawyers protect Microsoft from liabilities.
Their users are, in this case, a liability.
Would Microsoft care about youtube-dl? Aside from their recent gesturing towards open source, I can't see a scenario in which they'd even say anything. Considering how often youtube-dl has to be updated and re-downloaded, they might even be happy to get that load off GitHub.