Indeed – in fact the manual for the Harrison lathe (mine is an L5) advises setting the machine on its cabinet on a very slight slope towards the drain, using the cabinet levelling-screws provided. (They weren't on mine, and the holes in the base-plate didn't even have threads… I added some. Oh my goodness what a saga!).
This on a machine which was factory-matched to the planed top of the cabinet, no little bed-alignment screws a la Myford.
Modern cutting fluids don't rot and stink the place out as the older type of "suds" could (they attracted a particular bacteria). As a result, I never had to change the coolant in the hacksawing machine I used at work for some years; and I don't recall seeing that done very often on the other machine-tools, either.
As SillyOldDuffer asks though, is a pumped coolant system worth-while on our lathes or mills, generally used for fairly short periods and rather intermittently? Probably not. I'd considered a portable or central system for my Myford and Harrison lathes, and Myford mill, but I've enough projects wanting finishing to worry about replacing the present system, even though that's a worn paint-brush and old bean-tin.
Regarding Mike's comment about throwing out coolant with swarf, it's inevitable you will lose some like that, but if you wished to recover at least some, use a cheap, coarse kitchen sieve or old colander, and a bucket.