I agree with following the guidelines of the agency. That said, when I queried a few years back, very few of the agents accepted e-queries, so all of mine were snail-mailed. I did get 3 rejections within a week, one request for a partial, one for a full, and one (that I'd sent 5 pages per instructions) came back several weeks later with a positive rejection (as in this will find a home, but not for us). Eventually the other requests were rejected, too (also positively). I'm not sure that novel (the under the bed novel) is ready for prime time (though I only queried those 6). All told it was likely 6-8 weeks max.
Now I'm sure I'll use e-queries more, since it seems a lot of agents prefer them. Maybe novel #4 is the charm.