Well what you want to do is a bit tricky.
Lets take it from the top and clear some basics.
If you use a normal microphone driving it straight to the amplifier wont be a good option.
Microphone 's output impedance is 600ohm opposed to the 10kohm (hi-z) that the guitar amp is waiting for at the input.
So to cover the microphone part you would need a mic preamplifier to amplify the initial signal and then a re-amp box to make it hi-z so the amplifier can actually use it.
Now an amplifier has no broblem doing his job and giving you whatever sounds you're after, but judged by the case you may be into some trouble.
What i mean by trouble : a classical guitar is made to be a vibrant instrument as opposed to a solid one with a jack. The most common problems that arises in situations alike is feedback. Lots of it, uncontrollable loud feedback!
Also the sustain the body provides (which acts like a natural speaker) to the intonation will make the signal a bit constant and boomy losing detail and clarity.
Moreover, you should keep in mind that a guitar amp pretty much drops the highs an the lows, it just keeps the mids given the absence of a twitter.
You will be sending a midrange full signal(not a picky metal string edgy one) to a midrange speaker.
Bottom line is, i dont think thats any close to being a best practice scenario, but over the years ive experimented with various similar ideas. While sometimes it was an absolute failure, some others it was just what it needed, but at all times this is experimental.
If you want a good stable solution id recommend buying a high end piezo, i've had good luck with schertler http://www.schertler.com/en_IT/shop/pickups but they are a bit pricey too.
Good thing is that they provide a blue-tac style thingy that hooks it up to anything that produces sound without altering the instrument.
Classical instruments are not made to pass through amplifiers, they are just made to produce an end product sound and fill a nice sounding room with music! . (imho)