I'm not an expert on American presidents but would this get rid of the Reaganomics policies? Or the massive military build-ups? Neither of which helped the American economy and decayed the American government's ability to react to events in the future.
No, it would not have done much to Reaganomics or the military. The scandal broke in November 1986, nearly six years into the Reagan presidency. Reaganomics was well-entrenched. Oliver North's trial did not begin until 1989, after Reagan was out of office.
Look at the timetable between the Watergate break-in in 1972 to Nixon's resignation in 1974 under even stronger evidence for inevitable impeachment. If Reagan faces impeachment, it would likely take mere months off of his term. Meanwhile, George Bush would skillfully try to distance himself from the problem as he would run for president as an incumbent.
If Bush wins in 1988, the time line, including a continuation of economic and military policy, would not change.
Now, how could the scandal elevate the status of a Democratic candidate. The strongest OTL Democrat, Dukakis, proved to be very weak. The others?
Jesse Jackson - More racist polarization that Obama supporters could ever imagine.
Al Gore - Not in the limelight; potential to emerge within the Senate.
Dick Gebhardt - Typical congressman with too little exposure.
Paul Simon - Maybe best for the job, but too underspoken barring a Senate event.
Gary Hart - Political suicide for the Democratic party, given OTL.
Joe Biden - His veracity was already under question.
John Glenn - Too old.
Ted Kennedy - Too far left.
For the Democratic ticket to strengthen, something would have to happen to put Gore or Simon in the limelight.