I don't think you necessarily increase your hiring chances if you tell them that you'll pay your H-1 expenses. Heck, even if the company *desperately wants* to pay your H-1 expenses, you might not get an H-1 given the mess we are in right now.

Here's what I will recommend:

If the company has a history of sponsoring H-1, tell them that you will need it.

If the company doesn't have a history of sponsoring and they are not willing to do it for you and your getting that job depends on that factor alone, then tell them you don't need any sponsorship. ONE YEAR is a whole lot of time to make people change their minds. If they like your work (and even you as a person), I can say with a reasonable confidence that they will try to keep you!