If you were using water directly from your kitchen tap then this advice might have some credence. However, if you are using a Brita Filter Jug or better, then this is much less likely to be a problem.
Cycling water temp from cold to hot then back to cold again will precipitate some of the disolved solids on to the element and other parts of the boiler over time and will ultimately shorten the life of the element. If a Gaggia Baby has an Aluminium Boiler then this will probably corrode as well but not because of the temperature cycling but the pH.
I suppose it is possible that various boiler joins/gaskets might deteriorate more quickly over time too with regular temp. cycling but I dont think that this would be a major problem. The best preventative measures you can take to prolong the life of your boiler and water circuits is to use good quality water in the first instance, decalcify your water circuits every six months or so with Citric Acid (plenty of info around on how to do this) in accordance with your Operators Manual... maybe more often if the water you use is particularly hard (should then change your Brita Filter more often). Thats about all there is that I can think of at the moment, maybe someone else can add some more suggestions.
Personally, I wouldnt leave your Baby switched on all day as I dont believe it is necessary. Domestic espresso machines are designed to be used at very short notice, cleaned up and then switched off. I think it all comes down to water quality in the end and the investment of a Brita Filter Jug will save you heaps further on down the road so that would be my primary suggestion. All the best,