Hi Ruth... Yes, since the niece is listed as a last name of Adams with a birth listing of Texas, I would gather she is his niece, not hers.
As to the marriage license: as I say (probably too much) not everything is on the internet. I think your best bet is the Harris Co. Clerk's office (via snail mail and pay-the- fee). We have no evidence that they ever reside outside Harris Co. (Harris Co is Houston and Humble). I've checked the Harris Co. Clerk's office site and they have a marriage license database, but it only goes back to the 40's. You could also try the LDS Family History Centers and see if there is a microfilm of Harris Co. marriages (check www.familysearch.org and go to the catalog). That will take some time and still cost you, but it is an option. I did check a database that ends in 1909 and they weren't there, but it's an iffy database, so I wouldn't take the omission as a big deal (and on another point, keep in mind, they may not have married in Texas; especially since I can't find the 1910 census. Maybe Louisiana? Illinois? etc. etc).
Don't be too mislead by Charles Arthur dying in Hidalgo Co. He was probably just working on a rig when the accident happened...in fact his death certificate states the length of residence is 0 days 0 months and 0 years. (I spent 10 years in the "awl bidness," so I kinda understand the routine). The O.C. Adams that Joan points out as the informant is interesting, but I would imagine that it's a brother or cousin who was working with him. There's no reason to believe Clara Bell was in South Texas with him.
So..good luck! And as a side note, I wouldn't consider a 1909 marriage as "early" in Texas. That's actually more "middlin'" in the grand scheme of things.