Will Apple lock ARM Mac down? Probably.
Will ARM be the reason for the lock down? No.
What may happen is that apps that have been submitted and sold in the Mac App store could be recompiled for ARM - maybe by Apple and without the developer doing any work (especially if the developer used Apple's tools.) At that point - ARM apps that are available will only come from the Mac App store (at least initially) and could be locked down.
But there are a lot of apps that developers sell or distribute on their own (either through their website or through other distributors like SetApp) that may always be Intel-only.
So, it's quite conceivable that consumer-focused Macs (iMac, Macbook/Air) could be ARM and only get apps from the Mac App Store, while more Pro-focused Macs (Mini, iMac Pro, Macbook Pro, Mac Pro) stay with Intel and can get apps from anywhere (Mac App Store or through other sources) and have more choices available.
But my question has always been - why go through the trouble for a consumer-focused, locked-down ARM-based Mac when you can expand iPadOS for more Mac-like functionality, and provide features that would be difficult for the Mac (touch-screen controls, 2 in 1) all the while using the current, numerous iPad apps that already exist with no re-compile?