Although Spaghetti Squash and other squash isn't able to grow fully year round to keep enough supply the spaghetti squash and other squash are easy to store and keep so usually farmers can keep enough spaghetti squash available year round depending on how much spaghetti squash and other squash is grown that year.
So yes you should be able to find squash and spaghetti squash year round but sometimes supplies of spaghetti squash and other types of squash can be scarce.