Most bacteria tightly regulate the genes that enable them to take up DNA from their surroundings. This makes sense, since the uptake machinery is complicated, probably expensive to produce, and may interfere with other membrane functions, and since the benefits of DNA uptake may arise only under particular circumstances.
The regulatory signals include diverse physiological and environmental cues. In other posts I've discussed the signals that regulate H. influenzae competence, and here's a couple of recent reviews for Gram-negative and Gram-positive bacteria (http://onlinelibrary.wiley.com/doi/10.1111/j.1574-6976.2012.00353.x/abstract; http://www.annualreviews.org/eprint/F2P5NJ3vsbWfbPGtusKN/full/10.1146/annurev.micro.60.080805.142139). (Unfortunately neither is open access, sorry.)
But none of these bacteria are known to regulate competence by what should be the most important information - whether or not there's any DNA in their environment to take up. I say 'known to' because in fact there is almost no published information addressing this point, and the researchers I've contacted don't know of any relevant data.
It's possible that bacteria don't need this information because DNA is always within reach in their environments, but we don't really have data addressing this point either.
My lab has a new undergrad who doesn't yet have a project to work on. I wonder if he'd like to test this point, first in H. influenzae and then maybe in other competent species? Given the lack of positive evidence I'd expect negative results (external DNA doesn't affect competence), but I think this might be a case where negative results would be publishable.
The tests are tricky because addition of external DNA is also how we sensitively measure competence, so we might need a way to get rid of the 'inducing' DNA before measuring competence with the 'assaying' DNA. And good controls...