You can, but you probably should not. Mayonnaise is oil suspended in a small amount of water and egg yolk, and freezing shatters that suspension. The oil pools, the celery turns to wet string, and what you spoon out later is closer to soup than salad. Freeze the plain chicken instead.
What breaks when mayonnaise freezes

An emulsion holds millions of tiny oil droplets apart inside a water base, and egg yolk is what stops them from finding each other. Ice crystals push those droplets together until they merge. Once merged they stay merged, which is why stirring a thawed batch gives you slick streaks rather than the creamy body it had going in.
Yogurt and sour cream dressings fail for a different reason. Their protein network collapses under the pressure of freezing and the whey drains out. Avocado dressings hold together slightly better but brown badly. Nothing creamy passes through a freeze intact.
Which mix ins survive and which collapse
| Ingredient | After a freeze |
|---|---|
| Cooked chicken | Fine, slightly drier |
| Celery | Collapses and weeps water |
| Red onion | Fine, the bite gets sharper |
| Grapes | Deflate into loose skins |
| Apple | Browns and goes mealy |
| Toasted pecans | Fine, though they soften |
| Hard boiled egg | Whites turn rubbery |
| Dried cranberries | Fine |
| Fresh dill or parsley | Darkens, still tastes right |
| Mayonnaise | Splits into oil and water |
Freeze the filling, not the salad
- Poach or roast the chicken and pull it into shreds while it is still warm.
- Mix in only the sturdy parts, onion, herbs, dried fruit and a little of the poaching liquid.
- Hold back everything crunchy or creamy. Celery, grapes, apple, nuts and the dressing all get added on the day you eat it.
- Bag it flat in two cup portions, press the air out and write the date on it.
- Thaw overnight in the fridge, drain whatever pooled, then dress and finish.
Assembly takes about four minutes on the day, and the result tastes like a batch made from scratch. Two to three months is the quality window for the plain chicken. Nothing spoils while it sits frozen solid, the reason to eat it sooner is flavor.
If you already froze a dressed batch
It is not garbage, it is simply no longer a cold salad. Thaw it in the fridge, tip it into a sieve and let the broken oil and water drain away, then treat what remains as seasoned cooked chicken. A few fresh spoonfuls of mayonnaise will bind it well enough for a hot sandwich under the broiler. It also vanishes into a chicken melt, a filling for stuffed peppers, or a creamy casserole where a bit of separation goes unnoticed. What it will never do again is sit on a plate at a picnic looking the way it did before.