It depends. Some pubs will give you a year to complete the next book and some might not specify at all but have first right of refusal for the second or following books in the series.
Some writers finish the entire series before shopping book 1. It's appealing to some publishers if the series is already complete or if you at least have the second book done. They want to make sure you can deliver on the books as promised so already having other books done in the series can be a plus if they want the first one. Not to say you might not have to do rewrites, etc. But at least the foundation is there and it shows them you are serious. Sometimes authors don't come through as promised with a series and it leaves the publisher on the hook.
I always got book to book contracts with my series and I liked that because if things didn't work out I wasn't bound to send the pub another book. I never had a contract for an entire series at one time but my contracts did specify that if I did continue the series the publisher had first right of refusal of the next book meaning I had to at least show it to them first even if I wished to part ways. I never had the type of contract where I had to promise them a set amount of books in a series. When I write a series, I don't usually know how many books it will take to wrap it up. Usually I know by the middle of the series but I am not one who sets out to write a certain amount of books in a series before even writing one word of the first book. It has to come naturally. If the series should wrap up in three books, that's when it wraps up. If the series needs six or more books, then that's what I'll write. Different plots and things unfold while writing a series so for me it would be too difficult to write to a number of books.
For the two series I had with publishers, I just wrote the books and they sent the contracts each time I finished a new one.
As for is it doable, that depends on how fast you write. My average time to write a novel (60,000-80,000 words) is two weeks. I also outline. That's fast compared to some writers. Some writers need an entire year to finish a novel or at least a few months. It also depends on the length of the book and what else you got going on in your life that might interfere with your writing time.