Yep. Worcestershire does contain some vinegar, which would tend to neutralize the pH of the toothpaste, which is somewhat alkaline. (Too many dependent clauses?)
Toothpaste mostly contains a bit of pumice, which can be ground as fine or as coarse as the job warrants.
I generally prefer using abrasives for the purpose they are made. With toothpaste, for example, there's no telling whether Crest (or whoever) keeps the product mix constant. There are a lotta good metal polishes around.