Can you use an alkyd primer to seal a new concrete floor before using a floor paint?

A primer of any variety is meant to "Prime" a substrate! Dealing with a concrete floor new or aged, the single most important step in a successful floor covering, be it paint, vinyl, tiles, wood or carpeting, is to stop vapor emissions from migrating upward out of a slab. Very important with slab on grade construction with dehumidified [Air Conditioned] interior space. Low humidity interiors invite moisture laden outside [ambient air- relative humidity] to flow into the slab seeking the low R/H environment. This moisture vapor enters freely through the Gel-Pore/Capillry systems found in all concrete structures. Moisture carries with it, chemicals found in a concrete interior [primarily alkali's.

This moisture condenses on a cool concrete surface where it can form bubbles under vinyl, common paints or epoxy coatings. If you've heard stories about paint failures and peeling very soon after an application, most often a failure is associated with saponification or alkali burn. In any case moisture causes mold, destroys adhesives and is the root cause of flooring problems.

You need to water and vapor proof the concrete with a penetrating sealer that doesn't form a film or membrane and interfere with adhesion. Product that I use provides a 15 year waterproofing warranty, sprayed on in one application, low VOC for interior uses and accepts all mastic's or paint coatings. Not cheap but also works well. Beware of any sealer that allows for subsequent applications! (What happened to the first coat of it?) Also avoid any professed sealer product that cautions not to get it on glass or metals surfaces. They don't work!

I have seen terribly expensive clear epoxy materials [car dealerships] that you can see the moisture in the bubbles under the coating! There are three common test to demonstrate moisture vapor travel through a slab. They measure pounds of water vapor per 1000 sq.ft. and are The Bible for the flooring industry. Forget worrying about a primer, take care of waterproofing the concrete and you've won the battle!