At 5v5 only, no, there is no correlation between how frequently you take a shot versus how often those shots go in. As charlie1 said, better shooters tend to get more powerplay time, and powerplay shooting percentage is higher than 5v5 shooting percentage, so in the grand scheme there is probably a correlation, but at 5v5 it's so negligible that it may as well be 0.
Data included in the attached chart includes every forward to play 1000+ minutes of 5v5 hockey between 2007 and 2014 - 564 forwards, ~23,400 goals, ~254,000 shots.
edit: If you change the cutoff from 1,000 minutes to 5,000 minutes - ie, ensuring you only have quality NHL forwards (that brings the sample from 564 forwards to 165, the cutoff changes from "barely including Vasicek, Dandenault, Clune, Jacques" to "barely including Malhotra, Malone, Comeau, Peverly"), the correlation grows (from 0.008 to 0.044), but it's still less than 5% - and that's over 5,000 minutes. In a season where a forward might play 1/4 of that, it again may as well be 0. You can safely ignore it.