Only very marginally so, for those tiny shards of glass too small to go through the thicker wall. IME these are extremely rare, so I doubt you'll see fewer flats.

OTOH the thicker the wall the slower the natural bleed, or pressure loss over time. This will reduce the frequency of needing to top off somewhat. I only ride clinchers for commuting, and use the largest tube that fits for this very reason. Less stretch to fill the tire, means thicker walls and slower pressure bleed. I get by topping off only once a week.