Not so much, unfortunately. I was looking at a timeline of Nixon’s approval numbers recently. The Democrats initially proposed resolutions to impeach Nixon in '72, when his approval rating was ~60, and July '73, when it had dropped into the 40s, but they went nowhere. But by late October, after the “Saturday Night Massacre,” Nixon’s popularity had continued to plummet down into the low 30s. It was only then that impeachment resolutions, impeachment investigations and special prosecutor got started (and snowballed quite quickly). Nixon’s approval rating didn’t drop down too much after that point - never below about 25%.
Trump on the other hand, doesn’t seem to get below 40-something percent (depending on which survey one looks at) approval for long. (I find it inexplicable that his approval isn’t constantly dropping - but apparently so long as the economy doesn’t crater, white people are mostly fine with Trump.) The ceiling for Trump’s approval isn’t that high, it’s true, but, barring some economic catastrophe, the floor of his approval seems fairly set as well. The Fox News effect keeps his core support much bigger than Nixon’s was. Of course, Trump’s economic policies are damaging the economy, starting with his supporters, so we might see his support drop more.
I’d like to think that once Democrats start with impeachment investigations, what’s revealed will cause Trump to lose popularity. Either way, I think they should do it just because it’s the right thing to do, though.