The General Accounting Office, in a report highly critical of President Reagan's plan to abolish the Department of Energy, says a four-month study turned up no evidence to support the administration's claim that the action would save more than $400 million a year--or any lesser sum.

In fact, the GAO says the administration has failed to take into account "numerous" expenses that shifting most of DOE's functions to the Commerce Department would involve and has "not performed the detailed planning necessary" to effect a major reorganization efficiently.

The report, scheduled to be made public today, seems likely to doom any lingering hope of the Reagan administration to get legislation to abolish the Energy Department enacted in this session of Congress.

Introduced in the Senate two months ago, the administration's plan ran into reactions ranging from skepticism to outright hostility at the only hearing held. The White House has yet to find a sponsor to introduce the bill in the House.

In recent months, the administration has variously claimed that the reorganization would save $1.3 billion, $1 billion and $250 million over three years. But the GAO, in its report, said it found that "sufficient evidence has not been developed" by the administration to support any of the savings estimates.

The GAO said that when it reviewed the figures with administration officials, they agreed most of the envisaged reductions in personnel were "primarily related" to cutbacks in federal energy programs and were not linked to the proposed reorganization.

As to claimed efficiencies from merging the operations of the two Cabinet departments, the GAO said Commerce Department officials "had no specific explanation" of what types of automated systems could be merged to produce the $200 million savings cited by the administration.

In fact, the GAO concluded, "to the extent that it would be necessary to integrate systems, the difficulties of combining Energy's systems with those of Commerce would likely be substantial."

While the consolidation of these systems could eventually lead to economies, officials from both departments told the GAO they had not considered the "difficulties and expenses" associated with merging the systems in their savings estimates.

The GAO was even more skeptical of the administration's claim that the reorganization would save $50 million by tightening up the manner in which DOE audits private contractors' activities.

This figure, the GAO found, was based on Commerce's belief that DOE's "contractor-operated activities do not receive sufficient audit coverage." Commerce officials assumed that if these activities were more frequently and thoroughly audited, 1 percent of the $5 billion the Energy Department spends in this area could be saved.

"Commerce officials agreed this estimate is speculative and that a change in the methods of auditing contractors is not dependent upon a reorganization," the GAO said. Energy Department officials also expressed "concern about the accuracy of such a highly speculative estimate because it could give the incorrect impression that there is a significant amount of serious fraud, waste and abuse" in their programs.

The GAO also faulted planners of the reorganization for failing to take into account a wide range of costs--higher overtime costs, along with increased training and support-services expenses--that the administration's proposal would entail.

In sum, the GAO concluded that "the expenses of reorganization have not been assessed, and the current savings estimates are poorly documented and are based on inadequate implementation plans."

The GAO said, moreover, it had found that "the administration's preparations for making an effective transition" for Energy had been insufficient.

"The Department of Energy has not developed plans adequate for identifying and resolving potential reorganization problems and for ensuring that the proposed reorganization would be implemented as efficiently and effectively as possible," the report concluded.