Give it a try (e.g. at one rule and test it out). You can't proceed to place an order without choosing a shipping method, so that would prevent customers from skipping.
What makes it a bit tricky is the fact that Shopify asked for shipping address first. From a flow standpoint, in your situation it would be nice to have billing come first and then the question of second address for shipping is more like "Use same address for shipping or you are picking up". I think I've seen how people have used/tried to use CSS to swap positions. Above my pay grade.
