Will every email call my phone?

No. One call announces however many messages are waiting: “you have four messages”, then waits: press 1 and the new messages play in turn, one at a time. Eighty alerts arriving in two minutes because a switch dropped and every host behind it complained is one phone call announcing eighty messages, not eighty calls.

Email2Phone is a mailbox, not a dialer. If more messages arrive while you are still on the call, the next call carries the whole outstanding backlog rather than starting again from scratch. Tools that dial once per message do the opposite, and 3 a.m. is exactly when that difference matters.

There is no per-message throttle setting, because the mailbox model makes one largely unnecessary. For the case where one sender is the problem, the keypad’s advanced menu blocks that sender and clears its unread messages from the handset, mid-call.