Who else classes the Alpine Classic 200km as "general road bike" riding? I class "General road bike" riding as:
-commuting to work during the week
-the occasional weekend hills or coast ride
-runs to the TAB or the supermarket for milk, bread, wine and ciggies
Yeah but no.
If we're going to categorise, those things fall more into the "utility cycling" bucket.
As with all things, the right bike to use is the one you have... so if you have a road bike, there's no reason not to do those things on a road bike. Likewise if you have a squeaky hybrid, or a vintage singlespeed rescued from hard rubbish, or a $89.99 mountain bike from Big W.
Generally, though, "road cycling" is a more recreational activity. I guess your occasional weekend hills or coast ride falls into this bucket. As does the Alpine Classic, for those who are so inclined.
Those who get compulsively involved in recreational road riding tend to buy a bike designed for the purpose - often in addition to a general-purpose utility bike.
Why do a lot of people associate 'road bike' riding as some sort of sporting challenge? I hate getting asked "Oh, so you're a cyclist are you? Do you ride Beach Road on weekends? What do you think of Lance Armstrong? Do you wear lycra and shave your legs?"
Man - there is so much MORE to cycling than that crapola..... it's TRANSPORT
I guess that's a difference in interpretation of what is meant by "road cycling", versus "general cycling, on roads".
So, back to the OP: Would a bike set up for criterium/sprint racing be any good as a general road bike?
If that - with your interpretation of "general road bike" - is what the OP was asking, then my answer would be no... a crit/sprint race bike is not the best choice for a general purpose transport beater (with the caveat, as above, that whatever bike you have is the right bike if the alternative is no bike). I wouldn't ride a race bike to do the shopping or lock it up outside a pub.
It's more likely IMO that the OP was asking whether a race bike is suitable for "road cycling" - meaning, a recreational sporting-style activity. And the answer to that is "maybe". It's a more difficult question to answer, which is probably why it would be asked in the first place.
If you're happy having one bike to do everything, then good luck to you. Most of us have a broader fleet of more specialised bikes.