I've never played in a jam session so I don't have much right to comment. I do play in a couple of amateur bands. And though it may seem tempting to do my 'neck/mpc/reed' setup at home for rehearsals/gigs, I don't think I'd ever do it. Absolutely no criticism of those who do!
On the one hand, for me, setting up at the location is kind of a 'ritual': unpacking and setting up my sax stand, unpacking and setting up my sax, strap, mpc and reed. Making sure that my strap is supporting my sax mpc at the right height (and adjusting as necessary). Making sure that my reed and mpc are wet and there's a good seal.
And then - most importantly - finely adjusting the reed position on the mpc - so that I get the tone I want and can also play reasonably well over my usual range of low and high notes. These reed adjustments are usually 'parts of a mm' which I can adjust during a performance but I try to get a good start. If things aren't working out so well on the mpc/reed (despite adjustments) I often go back to minor strap adjustments.
And finally 'tuning'. Although my 'tuning' can vary slightly depending on whether my sax is warmer or colder, I try to get it within 'acceptable margins' from the get-go and maybe adjust slightly from there.
So basically, I don't think that I'd have 100% faith that any 'set-up' I'd did at home would remain an 'out-of-the-box' perfect setup at the location. If for no other reason, differences in temperature, humidity and slight differences to my 'strap height' (depending on what I wear and where I place my strap).
To repeat, I've never played in a jam session so I don't have much right to comment. At my band rehearsals, members are there 15-30 minutes beforehand so they've all gone through similar 'set-up rituals' before we start rehearsing.So forgive my ignorance but what's the rush that drives you towards being able to play within a few minutes/seconds?
How much more 'peace of mind' might it give you to turn up 15 minutes earlier? I find it difficult to imagine that all sax players jump on stage at the same time!
At least in my Pop/Rock Band, our 2 guitarists, drummer and keyboard player take a whole lot longer (20-25 minutes to 'set up' than I do on sax.
So my recommendation (without any experience or knowledge of the jam session) is just to do what feels most relaxed and comfortable to you. Don't feel any pressure that you have to copy other sax players. If you choose to prepare differently (at the location) then that's OK too. In the very worst case, you might not be 'first up' as a sax player. But I put it to you that a relaxed and comfortable 'setup' might help you enjoy your jam session participation more. Whether you're 1st, 2nd or 9th up!
Best wishes,
Mike
PS. IHMO, at any location, there's almost always a 'space' (such as outside or the gent's toilet!) where you can take the time to adjust your strap and reed as necessary. And 'tune' your sax. Yes, I've been there 🙂