It would be using some ram, it really depends on how android caches some data. I know that windows for example will take an application that is "sleeping" and write it to a page file to free up ram (mainly because windows runs on a 'free as much as you can policy'), however, linux will leave it in ram until space is needed (this is why if you run a linux system with 4gb of ram, you will notice that at least 75% of ram is used up after a few hours). As far as battery life goes, as long as the page isn't rendering anything, it shouldn't be using anything, RAM chips in general are a very very very low power device that is used to retain memory. As far as if there is a reason, it really depends on the type of user you are. If you are a heavy user of the browser, then no there is no reason to close a program like that, and android will recognize that and keep it 'sleeping' in the background. If you use the browser once in a while, android will recognize that as well, and shut it down. This is why sometimes you will open the browser and it will go to your homepage, and sometimes it will take you to the page you were previously at. Because our device has so much memory to play with, you will notice that a lot of applications will just sleep in the background. If you get a chance, hook up your incredible to the debugger on the PC. You will see a bunch of processes running, but most of them are using 0.00 - 0.01% cpu power ... generally these are 'signals' or 'pings' to let the program know 'hey, the OS is still alive, dont worry'.
Ever notice how when you bring your phone back from 'idle' the widgets seem to 'refresh'. For example, if you use the clock widget and are using clock #1, the hands reset? Thats pretty much what android does ... when things arent being used, they go to sleep in ram.
Hope that helps
edit:
It has always been a huge debate (i am a computer engineer) in computer technology as to which method is better: Free always vs Free when needed. There is a whole cult that says the former is best, another that says the latter. There is no right or wrong way, but if history is any indication, both are still around because one method isn't dramatically better or dramatically worse than the other.