If I am playing Jhin Legend and I have an Applied Researcher on the board and I play Consult the Past for three energy instead of four, does my Jhin Legend still proc to banish Consult the Past?

No, Virtuoso's ability will not let you banish Consult the Past.

Virtuoso checks "if you spent [4] or more" — that's the actual energy you paid, not the spell's printed cost. Applied Researchers reduces Consult the Past from 4 energy to 3 energy (its base cost of 4 minus the [1][A] discount, minimum 1). So you only spent 3 energy, which is below the threshold.

Your trigger fires (you played a spell), but the conditional check fails, so you don't get to banish it. If you want Virtuoso to work, you'd need to somehow spend 4+ energy on a single spell — discounts that lower the cost below that threshold mean you simply didn't spend enough.