Depends on when you pull plugs...if you wait after the plugs start to break down you can apply your crab prevention...or if you do get some crabgrass, you can always spray it too.
I know a local company would aerate each month and they had the best grass ever. Golf course and athletic fields aerate a lot too.
The nice thing with aeration in the Spring...is you pull your plugs 2 to 3 inches deep, the Spring rains come, and now instead of the new rain trying to work 2 to 3 inches of soil...with your plugs the water will now go down 3 to 5 inches....and now the water is deeper in your soil...your grass roots will grow towards the water...in turn making a healthier, more drought resistant, thicker, yard. Plus if you spread fertilizer after plugging....when the rain breaks down the fertilizer...now the holes with let the dissolved fertilizer go to your roots of the grass...making your yard spread and thicken also.
I think the only time you don't want to aerate is the summer....because of the heat, bugs, and disease can set in...unless you water or have an inground sprinkler system...but you would need to water to keep your yard moist...helping the plugs break down.
2013 Ford F450 Super Duty Truck
2010 Exmark Lazer Z 60" deck
2012 ExMark 30" Riding Aerator
2011 John Deere Pro Gator 2020a
2011 Lawn Solution Dual Hyrdo Aerator 24"
2011 Echo Handheld (trimmers to power pruners)
2007 Big Tex 4ft metal high side 7' x 12' Trailer
2012 PJ 7' x 16' Dump Trailer
2014 Vintage 8.5' x 24' Enclosed Trailer
2012 Ecolawn Applicator model 200 Compost Spreader