If you mean to ask if Nitrogen chemically bonds to H2O by co-valency, then no, it does not.
What happens with moisture in the atmosphere is that water molecules can fit between molecules of Nitrogen, Oxygen, and the few rare gasses that make up the air we breathe. When that air is cold, there is little space between the Nitrogen and Oxygen, so the atmosphere can hold very little moisture as there is not enough room between the air molecules. When the atmosphere is warm, it can hold a lot of moisture, because the molecules of Nitrogen and Oxygen have more distance between them, essentially "making room" for more moisture.
The dry Nitrogen we use has already had its moisture removed, but it is also warm from the van or from absorbing heat from the roof or the sun. So, we have a ready-made absorbing medium for moisture: plenty of room between the Nitrogen molecules because of the temperature, and little or no resident moisture already taking up the spaces.
When the Nitrogen is introduced into the system, the moisture easily finds spaces to take up, seeking osmotic equilibrium until the moisture is equally distributed throughout the gas.
Then, when we depressurize the system, the moisture is carried out with the departing Nitrogen.
But "clinging?" No, just finding a space for the departing ride.