Will I get into Tier 20?

No offense, but I don't have enough faith in that that score.
Try for 4870.

Seeing as how the week has just started and you're barely at the cutoff, no. In my experience, you need to go deathless to make T20.

The cutoff used to be around 4850, but I'd say it should be approaching 4880 now. Once you get into frequent 700's territory it gets way easier actually because you're using good units against less cancerous teams. I have almost no trouble getting deathless there but it's way harder down in the 690's imo.

I'm ranked ~3600 at 4896. I've been bouncing in and out of T20 for months with similar scores/ranks so that's at least a safe bet. It's not enough to ever keep me in T20 though. :P

No. You need to be in at least upper 4800's to stay, which basically requires a deathless run, or high merges and only 1-2 deaths. To stay in tier 20, you need to be up close to 5000 now. The line's been moving up quickly recently.

I think it took me 4900 to get T20 first time, but I manage to stay T20 pretty easily with scores around 4960.