Time

Could you get anything out of a plant with only 2 months of growing? Can you leave a plant untended for a week?

-Thanks
Apparition

Yes but not much and yes.

How much would you say?

Both questions depend on a lot of things. When your first frost (if any) will come in (If it your buds can't ripen, it's not even worth it). When the photoperiod in your area switches to 12/12 (The only way you'll get anything is if you immediately flower.) If it gets stunted at all, you'll get even less.
Even in my area, which is quite temperate. If it doesn't rain for a week in the middle of summer, I have to water them every day. Smaller plants are even less forgiving when it comes to watering. But if your conditions are right and it's not too hot, they'll prob. be good.
All in all it will probably be a waste of time,

Oh, not to mention the lower end of the flowering time is 60 days, so it's probable it won't finish at all.

Is there a way to speed up the growing process so to speak?

Well, there's some "Early" strains, which are autoflowering, but also require a certain amount of days, usually about 8 weeks so maybe those will do you good. Never tried them myself.

Go with dr.greethumbs iranian auto flower which is 90 days seed to finish or one of the less performing auto strains that are around 70 days. I would then use a large container amended with organic fertilizers and compost, because the more soil you have the longer you can go in between waterings, its better if you can get the roots of the plant underground as it will keep them cool(either dig a hole in the ground or dig a hole for the containers). You can also look into water absorbing polymers or a product called zeba which is made from cornstarch to help extend watering time.