I think some of it comes down to semantics, but in theory, with parallel compression you are leaving the high peak information alone (for the most part where it was originally at) but you raising up the lower peak information relative to it, so this does increase the weaker notes relative to the louder ones...and to me it's seems very similar to what you are describing with upwards compression. Seems like you would get the same end result.
Yeah, with parallel compression you are raising the weaker notes relative to the higher stuff, but it's not actually quite the same thing, and the end result would indeed be be a bit different than pure upward compression.
With the parallel compression, you may be raising the weaker notes compared to the higher ones, but you won't be changing the relationship of the quieter notes to each other. Let's say for sake of illustration that you have two notes below the threshold, one is 3dB down and the other is 6dB down from the thresh. When you apply parallel compression, those numbers will not change. While the dynamic range between them and the main energy of the upper peaks. will shorten, they will still be riding the same distance from each other and still be riding well below the RMS by the same varying degrees.
With upwards compression, however, the sub-threshold dynamics will be compressed upwards towards the threshold point, having the dual effect of both leveling out the volume of the weaker notes and pulling them up louder in relation to the signal RMS (assuming the RMS is above the weak notes). With the numbers given, if we apply an upwards compression of, say, 3:1 for example, with the threshold set somewhere around the RMS level, the two weak notes will now be 1dB and 2dB down from the threshold/RMS, much louder in relation to the average perceived level of the overall waveform and only one dB apart in volume between them, instead of 3dB. Plus there will have been zero change made to the stuff above the threshold, compared to a summing of wet and dry versions of it.
Now I'm getting confused.
Glen, can you find me a more complete description of this process? Compressed up seems like an oxymoron. If you are reducing the dynamic range below threshold that would be downward expansion. It seems like what your saying is that there is some sort of downward expansion and this component is fed back in without the component of the signal above the threshold?
Tom W described it pretty well, but here's a couple of pretty pictures that may help as well. The first is a kind of a schematic difference between upward and downward compression and upward and downward expansion. They are four different things:
And maybe this next one might help to show the difference between downwards and upward compression in another way. This is part of a display from Elemental Audio's Neodynium (a.k.a. Roger Nichol's Dynamizer). It shows two dynamic range zones set up, both with a threshold of -10dBFS. The top (red) zone I have set up from 0dBFS to -10dBFS, and has meen configured with a downward compression of 3:1 applied to it, which is graphically represented by the narrowing down to the right, The lower (orange) zone, I set up from -10 to -20dBFS also has 3:1 compression applied to it, but it is an upward compression instead of a downward one, represented by the narrowing of the zone upwards on the right.
For the OPs situation, I would use Neodynum (my favorite compression plug, BTW; it has a LOT more than just what you see here) set up with one dynamics zone set up similar to the orange zone in order to upward compress the weak notes, evening out their volume somewhat while leaving the peak stuff completely alone. The threshold would depend upon the actual recording, and the low end of the zone would be just low enough to cover the notes I'd need to bolster.
G.
. The tool is typically referred to as a "dynamics processor". I don't know PT well enough to say if it came with one or not, but I'd be extremely surprised if it didn't automatically come with one right out of the box, because most other editors do. 
