This comes up in Bad Axe Games's
Trailblazer. It recommends that if you want to make a monster into an "elite" monster, double its hit points (and give it 1 action point) - this doesn't increase their CR.
Since monsters use the average of their Hit Dice, which is just slightly over half, this is almost the same as giving them maximum hit points per die (it's actually a bit more, since Trailblazer's method also doubles hit points from a high Con score). Hence, that seems to lay down that maximum hp alone doesn't warrant a CR increase.
It's complicated, and as Crothian mentioned, highly dependent on the critter in question. For creatures packing asymmetric threats (think beholder, or mind flayer) the extra hit points will grant longevity, which permits the critter more rounds to live and hence more actions, which ultimately exposes the players to more danger.
Lanchester's Square Law gets involved here, too, but let's not get too deep into that.
Rather, in summary of Lanchester's, consider that
two creatures have the same number of hit points as
one creature with double hit points-- but two creatures have twice as many actions, and they force the players to divide their actions.
As we all know by now, two creatures increases the EL by +2-- ergo the increase must be less than CR+2, and I posit it's considerably less.
One creature-- albeit with twice as many hit points-- has half as many actions and is likely to die twice as fast under the combined fire of 4 PCs.
You can't
ignore the effects of doubling/maximizing hit points, but neither does it necessarily raise the CR by +1. In concert with other things that make an encounter more difficult (allied creatures, terrain, etc.), perhaps it's worth a +1 bump.
My inclination is to round it down to +0-- but I am a rat bastard.