And will it make you smell better if you eat no onions, shallots, garlic, or leeks?

Subjective. The question is whether you want to give up an enjoyable element of dining to relieve bad breath when a toothbrush or mouthwash would be effective. As for general odor, people who eat lots and lots of garlic will develop a body odor which is distinct, as anyone who has lived in korea will tell you, but whether this is distasteful is a subjective opinion.