Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure.
Does over stacking have any impact on melee?
Sure: you risk losing more troops to a single roll.
...couldn't a player send, for example, three full squads and two leaders into a melee hex...
if it was likely that the hex would not be in LOS for a fire attack for a turn?
That has less to do with the overstacking mechanic itself and more to do with your opponent not providing adequate protective fire for his forwardmost positions. If you can pull this off it is likely your opponent's setup was suboptimal (or you have already neutralized the position that was covering the hex you intend to melee into oblivion).