Well, everyone is different, but no,
I don't experience it that way. I see it as love... which is often complicated - and not always romantic. It can represent other types of relationships as well or other types of love. Or passion/sex. (And choices, of course, though I kind of don't like that meaning. It's definitely there though.)
Six of cups is usually very simple and joyous. It's somehow more pure... Not meaning without passion or sex, but just like what you wrote above
I never get that feeling off the Lovers, nor am I ever in that situation when the Lovers appears. lol I don't know why. The different nuances of how and when different cards show themselves to different people is so interesting, isn't it?