For planning purposes you'll want to carefully read the program announcement from the NSF to see if they state a policy on deferment. For instance, in Instructions for Preparing and Submitting
Mathematical Sciences Postdoctoral Research Fellowships (MSPRF):
The postdoctoral appointment must start between June 1 and October 1
of the year of the award.
The GRFP guidelines (for graduate students - not a post doc), just to show another example and outline the NSF's typical policies, has a similar provision:
May I defer my Fellowship?
No. There is no general Fellowship deferral - only approved Military
or Medical Deferrals. Deferrals are different from Reserve years.
While on deferral, a Fellow's clock stops, i.e., the remaining time
available for Tenure or Reserve periods is not affected. Reserve years
are counted in the 5-year period allowed for the Fellowship.
Regardless of published policy, "you can always ask", as there may be some special exception granted because of your particular situation and proposal. But the official policies will give you a reasonable expectation of what to expect - if they say you can, you can, but if they say you can't, you might not be able to (but it's not utterly impossible - just less likely).
If someone who has been in a similar situation and requested a deferral (even against stated policy) could share their experience that would be even better, but the official printed guidelines is always your best starting place.