Yes.
The practice you're describing -- raising prices after driving competitors out of business by selling below cost -- is known as "predatory pricing," and it is a classic monopolistic practice outlawed by Section 2 of the Sherman Act and by the Robinson-Patman Act:
Predatory pricing may be defined as pricing below an appropriate measure of cost for the purpose of eliminating competitors in the short run and reducing competition in the long run. It is a practice that harms both competitors and competition. In contrast to price cutting aimed simply at increasing market share, predatory pricing has as its aim the elimination of competition. Predatory pricing is thus a practice "inimical to the purposes of the antitrust laws, and one capable of inflicting antitrust injury.
Cargill, Inc. v. Monfort of Colorado, Inc., 479 U.S. 104, 117-18 (1986)
Federal courts' willingness to enforce the Sherman Act against predatory pricers has varied drastically over the years, but the U.S. Supreme Court laid out limits on their authority in Brooke Group Ltd. v. Brown Williamson Tobacco Corp., 509 U.S. 209, 113 S. Ct. 2578 (1993):
“First, a plaintiff seeking to establish competitive injury resulting from a rival's low prices must prove that the prices complained of are below an appropriate measure of its rival's costs.” The Supreme Court has not yet told us what is the "appropriate measure" of costs, but there are arguments that it should look at marginal costs, average variable costs, long-run average incremental costs, and average avoidable costs.
"The second prerequisite to holding a competitor liable under the antitrust laws for charging low prices is a demonstration that the competitor had a reasonable prospect, or, under § 2 of the Sherman Act, a dangerous probability, of recouping its investment in below-cost prices." In other words, the courts are going to ask how likely it was that the pricing strategy was likely to result in eventual profits that offset whatever losses resulted first.
Many cases seem to fall apart on the second prong, as the courts often find that although a business was pricing below cost, the pricing structure did not result or was unlikely to result in an eventual recovery of those losses. That was the case in Matsushita Elec. Indus. Co. v. Zenith Radio, 475 U.S. 574 (1986): Zenith alleged that Matsushita had been charging artificially low prices on TVs exported to the United States for 20-plus years, but the Court ruled for Matsushita, holding that the plaintiffs hadn't produced actual evidence of an agreement to lower prices, and that the fact that the prices were still artificially low suggested that the conpsiracy to drive competitors out of the market was either failing or nonexistent:
The predatory pricing scheme that this conduct is said to prove is one that makes no practical sense: it calls for petitioners to destroy companies larger and better established than themselves, a goal that remains far distant more than two decades after the conspiracy's birth. Even had they succeeded in obtaining their monopoly, there is nothing in the record to suggest that they could recover the losses they would need to sustain along the way. In sum, in light of the absence of any rational motive to conspire, neither petitioners' pricing practices, nor their conduct in the Japanese market, nor their agreements respecting prices and distribution in the American market, suffice to create a "genuine issue for trial."
In the hypothetical you offer, though, there is some sort of "projection" indicating that the strategy may actually be successful. Depending on how reliable that projection is, and how likely it projects the recovery to be, adopting the strategy could therefore be a violation of either the Sherman Act or the Robinson-Patman Act.