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The possible snag with that plan is that in order to enter as a VWP traveler by air, you're supposed to have a round-trip ticket whereby you will end up somewhere that is not Canada or Mexico.
Based on the anecdotal evidence available to us, this rule is not really enforced consistently. However, it does provide an impeccable ground for the border officer to deny you entry if he doesn't like the color of your shoes. And it is possible that the airline will refuse boarding you if you have neither a valid visa nor a round-trip ticket.
If you do attempt this plan, you should expect that the border officer will notice the future visa in your passport, and be prepared to convince him that (a) you're not going to start work before you're allowed to, and (b) you will actually make the visa run later, because the rules do not allow you to change from VWP to H-1B status while in the US. At the least, bring documentation of your job offer with its start date, and preferably also tickets for the short trip to Canada or Mexico.