Yes, radar can impact your C and KU reception. The size and function of most commercial airports isn't likely to affect the intensity of the interference. Most only have regional radar and communications before handing the flight off to another control center.
The commercial airport interference is outside of the downlink frequencies, but if strong enough, can easily overload the LNB or receiver's front end. Often, just the selection of a dish location can provide line of sight shielding from interference. LNBs and waveguide filters are often used to filter out this interference.
Best to have a qualified RF engineer perform a site survey before any significant investment. If that isn't an option, connect wideband, unfiltered LNBFs (both a C-band and a KU band types) to a quality spectrum analyzer and point the feedhorns towards the horizon in 360 degrees and look for increases in the noise floor and spikes. Repeat from different locations on the property and compare the readings.