Carpet and underlay on concrete stairs?

I live in a cottage flat and have stairs leading up into my flat, they are concrete painted red steps. I have just bought carpet for the stairs and a can of spray adhesive to stick the carpet to the stairs. I have just aquired some underlay and was hoping to use that also. Would it work if I spray the underlay with adhesive, stick it to the steps then leave it a day to stick properly then spray the carpet with the adhesive and stick that to the underlay??