You CAN win with just one book.
It will just take much longer and how much longer depends on the book.
You probably CAN do it, but why would you want to? Take advantage of the options available out there and diversify your funds, that way you're not forced into some lines at some books on some plays because of the constraint of getting down.
By staying diversified you can also move money around a needed, based on where you buy what lines, so that you can at times increase and decrease your balances at different books. This is also how you diversify, by balancing them out. Not going to go into much detail there, it's a little more advanced.
But beware, when it comes to off market lines and arbs, or buying both sides, some books are always in a certain position.
I'm sure there are bettors reading this, that are funded at many books, and even though they are winning overall, there always seems to be a couple of books where he/she is constantly reloading, while other accounts at other books swell and need to take withdrawals.
There's one book in particular that will take your hedge or arb, but for some reason that's always the bet that loses. Even if there is profit overall between accounts. Because they are sharp.
One point here is that so much more can be done when you are diversifed account wise, there aren't just more betting options out there, there become more ways to use those options.