No. There should be no adhesive between

the weather strip and your windshield glass. The weather strip is supposed to be removable. Did water get inside your car? If you see water inside your car, then it must be caused by adhesives underneath your windshield glass.

If you really want to add some adhesive, you can get some black Liquid Nail with urethane. Make sure you use masking tapes when you apply it. Otherwise, it will look ugly.