Enhancing audio data from moving magnet turntable?

Simple answer - no.

But let's expand on that a bit, so you know why, because it's a two part answer, the second part of which Audition could potentially cope with, if it wasn't for the over-riding problems of the first part...

The initial problem is that the signal from the cartridge is at a very low level, and applying that to a normal sound-card input would just have it lost completely in noise; these inputs are designed to work with inputs at least two orders of magnitude higher in terms of signal strength. Not only that, but they have completely the wrong impedance for any sort of phono cartridge, so even if you could get a usable signal, it wouldn't sound very good because the cartridge resonance wouldn't be correctly damped. Phono preamps are designed to deal with this; they have much lower noise, and are designed for low-level signals.

The second thing they do is provide EQ for the cartridge. This is in a standardised form based on a RIAA curve, and if you had an un-EQ'ed output from a preamp, Audition could technically manage this, although you won't find a preset, because nobody in their right mind would ever want to do this; it would be far from ideal. The reason for this is that the other thing that happens in the preamp is that the EQ is integrated in the design of it, and the noise performance is optimised for it. The nature of the EQ is that the bass gets a hefty boost, and if you just used an ordinary but sensitive preamp, you'd end up with a noise performance you really didn't like very much afterwards.

So this is why phono preamps exist - because they are the only correct way to achieve the results, I'm afraid. No getting round it at all...

So when you said "When using a moving magnet cartridge turntable for playback on your stereo set you usually need a device called phono pre amp" the word 'usually' is, I'm afraid, incorrect - it is always if you want to be able to listen to the results!