We can't know for certain.
- There is nothing to suggest that the Quantum Realm shown in Ant-Man and Wasp behaves like it's comic book counterpart, the microverse.
- Current comic continuity has not (to the best of my knowledge) touched on how the Soul Gems (Comic equivalent to Infinity Stones in the MCU) interact with the Microverse.
- The MCU has shown no evidence for the Quantum Realm being affected or unaffected by the infinity stones.
I will try to answer the questions above as logically as possible, but be forewarned that this is all speculation, as no hard information on the topic is available.
Is it possible that Ant-Man being in the Quantum realm at this moment
could mean that Dr. Strange couldn't perceive that he had survived in
his mental evaluation of future outcomes - and therefore couldn't
explore possible futures involving Ant-Man?
Dr. Strange is not "theorizing" or running a simulation of what will happen. He is using the Time Stone to view ~all~ Fourteen million, six hundred and five of the possible timelines:
I went forward in time. To view alternate futures. To see all the possible outcomes of the coming conflict.
Because he was actually traveling through time, he was not perceiving whether he survived or did not. It is possible that he was temporarily unaware that Lang survived, due to Lang being unreachable, but he saw all the futures that could happen, including those that have Lang joining the fight (assuming he does join the fight in any of the alternate futures).
Is it possible also that Ant-Man was spared because he was in the
Quantum realm at that time, a reality that Thanos might not be able to
impact even with the Infinity Stones?
I see nothing to indicate that the quantum realm would be beyond Thanos' power to impact, except for this quote by Hank Pym:
...a reality where all concepts of time and space become irrelevant as
you shrink for all eternity
However, we've already seen an MCU example of the Infinity Stones (specifically the Time Stone) functioning in a "reality without the concept of time and space" when Strange created a time loop within Dormamu's realm. If the Time stone can still affect a realm beyond time and beyond space, we have no evidence to assume that the other stones would be unable to affect it.