Spaghetti squash are a winter squash like butternut. Like other winter squash they are slower growing than summer squash like zucchini. Your packet should tell you days to maturity. Count backwards from when you expect frost and that tells you the latest you can plant it.
I checked and found days to maturity for different varieties of spaghetti squash listed as anywhere from 85 to 120. So assuming yours is on the quick end of that, the question is do you have three months until frost comes? If not you probably don't have time to do a fall crop of spaghetti squash. Save your seeds and plant them in spring once the ground is warm.
Plenty of things you could plant now for a fall crop. Here's a planting schedule: https://www.thevegetablegarden.info/resources/planting-schedules/zones-7-8-planting-schedule
Most definitely makes sense. The packet of seeds is generic, so it has no time or maturity info on it, someone at work gave it to me (she never grown it either)... But based on the maturity dates you mentioned - I really doubt that I have close to 90 days before the frost... Spring time it is =)