Not necessarily - the argument of "passing on the tax to the consumer" doesn't really hold up in a free market. If a good or manufactured product faces many competitors in the same market, and the prices are competitive, then the company will be more reluctant to raise the price, especially if there is little else differentiating it from its competitors. Companies act individually. They don't always act in concert.
Lets say, for instance, you have companies A, B, and C. All companies perform the same amount of work offshore, which translates into roughly the same amount of cost savings. Lets say that we now tax all three companies along the same lines of the first scenario which you have described above. Company A is the first to "pass" its tax to the consumer, and is quickly followed suit by Company B, which also "passes" its tax to the consumer, but only passes about half of the tax.
Company C is now in an interesting position. Assuming the goods of all three companies are the same, Company C now has the cheapest product on the market. It may be making less net profit per item sold, but there is a good chance that the sales for its product will increase, because it is now the cheapest alternative. It can now choose to hold its price instead of "passing the tax" to make the difference on the loss in profit from the tax, banking on higher sales because the competition has increased the price of their products.
Disregarding the companies themselves, as far as the government is concerned, it is probably more interested in getting citizens off unemployment and collecting off their income taxes than making money from corporate taxes incurred from offshoring, so analyzing how much the government would benefit from tax revenue pursues the wrong path of inquiry. The national and state governments make far more money off of income tax.
Lastly, a tax such as this would serve as a deterrent for future offshoring, which is a real concern. If a company notices that after construction, moving, and re-organizational costs, that it will also be subject to a tax that may easily be raised, then it will think more carefully about offshoring. We have lost a great many jobs, but we absolutely cannot afford to shed them in similar numbers in the future. Not all of it was due to offshoring, but a lot of the jobs that we have lost that will be difficult to replace were. Preventing that from happening again is a good idea.