A sales tax in place would act to impede such activity more than the current situation.
Increasing a general sales tax might well be more difficult. A targeted sales tax that goes after items that are only accessible to people with substantial disposable income (aka "the rich") would not cause a general outcry. How many people complained about the "luxury tax" on large boats? Almost nobody. The "rich" responded by not buying the boats. The boat manufacturers responded by folding up shop. The idiots who foisted the tax on the boat "consumers" made less money and put lots of boat manufacturing workers on the street. The failed tax attempt was later rescinded.