Are they a good training aid? I'd say so, a mixed on/off road session on a crosser gives you a good workout, though that's probably on part due to the battering you get.
And IMO you'll not feel the benefits of a cross bike if you buy one this time of the year. I'm not saying they're rubbish in the dry as they're still great, but they come into their own in the winter big time.
I think in all honesty if you're asking all these questions then you really need to get gears.
I'm going to buy a s/s crosser this winter as a second race bike and general foul weather do it all bike, but looking back on what I've done on my crosser i.e CX races, sportives, reliability trials, training runs and general trail rides I'm glad I've had gears.