Beware - technical stuff...

Machine learning methods are actually used for more than 30 years in particle physics. They are not really based on image recognition, but more on the fact that some properties of the collisions are different for the signal and the background. The output then consists in a decision of the event being more signal-like or background-like.

do the searching algorithms become more efficient as more collisions are examined over time?

Yes and no. You have statistical uncertainties that are reduced with the amount of collisions. But you also have a bunch of uncertainties inherent to the method and those are independent of the amount of collisions. For many searches, we are now systematics limited and not statistics limited anymore. Therefore, we really need huge improvements in the analysis techniques to get a better sensitivity to the signals.