If your out-of-range saddle is under a plain string, you will probably be okay if you change string gauge (without changing action). If the out-of-range saddle is under a wound string, then it could go either way.
Ideally speaking, gauge does not affect the intonation of unwound strings which are made of the same material and tuned to the same note in the same string position of the same guitar. This is because although there is more tension in a thicker string, the stress is the same. A string which has twice the cross area has twice the mass, and so it needs twice the tension to get to the same pitch. The result is that the stress (force per unit cross-sectional area) is the same. Stress is measured in the same units as pressure: Pascals.
If the action is also the same, then it means that the elongation of the two strings is also the same due to the same geometry of the situation: when we fret either one at the same fret, we are elongating it by the same amount. Fractional elongation of a material is called strain. We are adding the same amount of strain to the thicker or thinner string, and the change in stress depends only on the strain and the material's elastic modulus.
Intuitively, if the string has, say, twice the cross-sectional area, then it's somewhat as if you had two strings of the original size in parallel. Now there are going to be factors that creep in that will make some small difference, like neck relief changing under stress, the fact that the string is not an ideal string but actually a long skinny bar (and so a string with twice the area perhaps does not require exactly twice the tension to get to the same pitch), and material differences.
Material makes a difference because different materials require more or less tension to stretch the same amount (that elastic modulus thing again). For instance nylon strings for classical guitars have a low elastic modulus. They strain easily under low stress and so their pitch does not change much when they are fretted. For the same reason they do not respond to string bending very well.
If the unwound string is made of two materials (like via plating applied to a core) that also creates the possibility that the intonation will change, since their ratio will probably be different in the different diameter.
Things are far less clear with the wound strings. The winding contributes to mass, thereby lowering pitch, but does not contribute much to the string tension, which is carried almost entirely by the core. Intonation almost certainly will change with a change of unwound gauge, or from change from plain to wound or vice versa because the thickness of the core as well as the amount of mass added from windings are changing simultaneously, and so the stress in the plain core will certainly be different at pitch, even if it is exactly the same material. Since the proportionality of mass and tension is not maintained, the intonation could go either way.
So if you're changing gauges without changing action, and keeping three plain strings plain, then you can expect not to have to do much, if anything, in regard to the three plain strings if they are the same "series" from the same manufacturer (same material). The saddles for the wound ones will likely need more adjustment.
I have found this to be approximately the case in actual experience, when changing among .009, .010 and .011. The theory, of course, goes out the window if you adjust action and/or neck relief.