Would this router work on milling out small aluminum parts?

You can buy a cheap small milling machine from Harbor Fright.

You might (and that is a very big might) be able to do that using carbide router bits. However as a retired master machinist and long time woodworker I forsee several problems. First of all you need a lubricant of some type to cool and lubricate the material being cut and the cutting tool when machining aluminum. Most of these are either water soluble compounds or in some cases simply petroleum distillates (I have seen older time machinists use kerosene) You can imagine the issues when this gets into the router motor. Secondly, the grade of carbide used in woodworking tools is different from that in metalworking machine tooling. Not going to finish well or last long. Use a milling machine for your aluminum parts and don't ruin a good router.