An easier way to look at this: (nothing to lose): something to gain or (nothing to gain): something to lose. When faced with it in this light, it becomes clear that the choice is to have something to gain rather than something to lose. Or rather, to choose nothing to lose than nothing to gain.

Speaking as someone who drinks too much beer, the answer is clearly yes, since beer is rational. Granted, the consumer thereof may not be, but that's a different matter entirely.

I'm sure that at some point we have all consumed irrational quantities of beer. That is, quantities of beer which cannot be expressed as the ratio of two integers. Clearly the absence of such quantities would greatly complicate any recipes for beer pi(e).

It is worse to have nothing to lose. Having nothing to gain implies that you might have already gained it all.

Pardon me while I go buy a lottery ticket.

To be contrary, second question first: Yes. Drinking too much beer makes you as rational as you can be after drinking too much beer, hence, beerational. See also, beer goggles.

My answer to the first question: it would be worse to have nothing to gain, because I would have no motivation to get up in the morning. YMMV, but that's what keeps me going, the idea that each day provides the opportunity for some kind of gain. If I've got it all and have nothing more to learn, I might as well be dead.