Will shoppers be stopped from signing up once I reach my plan's customer limit?

No. The note at the top of Customers → Manage Customers ("… customers used on your plan") is information only. Storefront sign-ups and guest checkouts keep creating accounts even after you reach the number.

When you are at or over the limit, the note turns amber and shows an Upgrade link to your Subscription page. If you want the plan to match your real customer count, upgrade from there. The note is hidden when your plan has no customer limit.