sugarfree,
The clarification process your recipes describe is designed for the yeast in cider to 'clean up' any undesirable flavours that may have been produced during vigorous fermentation, then drop out along with other suspended solids.
Whilst the first part of this statement is true, this process is mainly to make the cider 'look clearer' (think cloudy vs bright cider) and has only a small effect on flavour.
In terms of carbonation, given two ciders that have the same amount of CO2 dissolved in them, one cloudy and one bright, the cloudy cider would appear to be more carbonated when poured because of the greater amount of nucleation sites for CO2 bubbles to form.
In terms of your question... I would not filter through coffee grind filter pads. I doubt that they have a fine enough filtrate rating (micron level) to remove all of the yeast cells in the cider and I cant think of a way of doing it with oxygenating my newly finished apple brew.
Oxygenation of beer/cider/wine on the so called cold side of brewing is unadvisable as you drastically reduce the storage time of whatever you've so lovingly concocted (even below 24 hrs if oxygenated well). There is also the risk of introducing an infection but this is somewhat reduced at the end of fermentation due to the alcohol content of the fermented liquid.
Having said this... if its a small amount and you just want to see what happens... go for it. I wouldn't with a larger batch.
hope this helps.