How long will Tiramisú made with raw egg keep?

According to the USDA, opened eggs kept under 40 degrees F (5 C) will remain safe up to 3-4 days. Acids and alcohols will slow bacterial growth, giving you another day or two, but bacteria are remarkably sturdy, such that I would not count on the Madeira or other liqueur to "sterilize" the food. Also, bacteria are equally happy growing in most egg substitutes -- protein is protein -- so the same safety rules apply. (If your egg substitute is purely starch-based, such as the one made by Ener-G, you might have an extra safety margin, but I don't know how good the tiramisu will be.)

One way to improve your chances of avoiding food poisoning from bacterial contamination is to cook (Pasteurize) your eggs. Many versions of tiramisu use a cooked zabaglione, made by beating eggs and sugar in a double boiler, whisking in the alcohol, and stirring until the mixture thickens (at about 160-165 F; 71-74 C), then chill very rapidly. Of course, this won't affect bacteria that get into your dessert through other means, like Aunt Marge sneezing on the cookies, but at least it will help ensure the eggs are not the source.

Stilltasty.com gives 2-4 days on raw eggs in the fridge - so I'd expect the same.

Egg substitutes may trade some flavor for longer shelf life.

This, among other depends on your use of alcohol in the Tiramisu. Without any Marsala or other alcohol you could expect the same lifetime as raw eggs (I throw out anything older than 2 days) with the added alcohol its disinfecting properties would prolong the lifetime with a couple of days. But I think the Tiramisu is best within the first two days.