It is kind of important to use everyone in the game a little but the game does tend to force you to use certain story relevant characters in the first half for good portions of it. It becomes more important to level everyone in the second half because a few dungeons use a mechanic where you have two or more parties of four to complete, so it helps to use everyone a little.

Your party doesn't technically level with your main party when not in use, unless they are removed from play in story mode, and then they do get a small boost in levels with your party average when they rejoin the party if memory serves me correct. On the brightside, VI is relatively easy as a game and you can beat the whole game with the right set-up in your 30-40 level range. Past level 40 just makes the game a breeze so honestly level grinding is not a big deal despite the large cast. There are no dual-style battles where an underleveled character can potentially make the game unwinnable, but there is a point midway through the game where the difficulty does spike a little and your left with one character. It's possible to simply run from battle until you can get to town if need be so don't fret over this.

VII doesn't have this issue as unused party members do level slowly in reserve and frankly your Materia is more important than your party. VIII is a bit weird in that levels are bad because enemies grow in strength with your party so you genuinely want to stay low level until you get better with the Junction System. Like VII, your characters Junctions are more important than their levels or weapon upgrades.

IX also lacks any real moment where you can get screwed like this, in fact the one character who does get shortchanged levels in the game actually has a short segment in the game designed around power-leveling them to the rest of the parties standard. So yeah, no worries.