Can you use minced garlic instead of the clove(s)? And, does the clam juice really add that much to the taste of the finished dish?

The recipe calls for the cloves to be minced, so if you have the ready made minced garlic on hand- that's fine. It usually isn't as strong as the freshly minced cloves, but you can adjust to your own tastes. I'm not sure what clam juice you are referring to, because the recipe isn't calling for any. It calls for oyster sauce, which I wonder if you have confused with clam?? The answer to that would be yes, it does add to the finished dish. Oyster sauce brings a concentrated, umami, seafoody flavor that enhances the shrimp and noodles. Otherwise, it will just be some garlicky and salty spaghetti with shrimp piled on top.