A difference between what Gel'fand did and what the Germans were doing is that in 1930s-style algebraic geometry you had the basic geometric spaces of interest in front of you at the start.  Gel'fand, on the other hand, was starting with suitable classes of rings (like commutative Banach algebras) and had to create an associated abstract space on which the ring could be viewed as a ring of functions.  And he was very successful in pursuing this idea.   For comparison, the Wikipedia reference on schemes says Krull had some early (forgotten?)  ideas about spaces of prime ideals, but gave up on them because he didn't have a clear motivation. At least Gel'fand's work showed that the concept of an abstract space of ideals on which a ring becomes a ring of functions was something you could really get mileage out of.  It might not have had an *enormous* influence in algebraic geometry, but it was a basic successful example of the direction from rings to spaces (rather than the other way around) that the leading French algebraic geometers were all aware of.  

There is an article by Dieudonne on the history of algebraic geometry in Amer. Math. Monthly 79 (1972), 827--866 (see http://www.jstor.org/stable/pdfplus/2317664.pdf) in which he writes *nothing* about the work of Gelfand.  

There is an article by Kolmogorov in 1951 about Gel'fand's work (for which he was getting the Stalin prize -- whoo hoo!) in which he writes about the task of finding a space on which a ring can be realized as a ring of functions, and while he writes about algebra he says *nothing* about algebraic geometry.  (See http://www.mathnet.ru/php/getFT.phtml?jrnid=rm&paperid=6872&what=fullt&option_lang=rus, but it's in Russian.) An article by Fomin, Kolmogorov, Shilov, and Vishik marking Gel'fand's 50th birthday (see http://www.mathnet.ru/php/getFT.phtmljrnid=rm&paperid=6872&what=fullt&option_lang=rus, more Russian) also says *nothing* about algebraic geometry.  

Is it conceivable Gel'fand did his work without knowing of the role of maximal ideals as points in algebraic geometry?  Sure.  First of all, the school around Kolmogorov didn't have interests in algebraic geometry. Second of all,  Gel'fand's work on commutative Banach algebras had a specific goal that presumably focused his attention on maximal ideals: find a shorter proof of a theorem of Wiener on nonvanishing Fourier series. (Look at http://mat.iitm.ac.in/home/shk/public_html/wiener1.pdf, which is *not* in Russian. :)) A nonvanishing function is a unit in a ring of functions, and algebraically the units are the elements lying outside any maximal ideal. He probably obtained the idea that a maximal ideal in a ring of functions should be the functions vanishing at one point from some concrete examples.