While playing alternating bass is it improper to count the I and V as eighth notes, i.e. (I-strum-V-strum-I-strum-V-strum) where the strum would be the 'and' of the beat? Would this be incorrect because it doubles the tempo?
Terms are confused in this question. I and V in key C, for example, are chords C and G. You probably mean notes C and G - quite different - and shown as 1 and 5.
In 4/4 it's common to play 1 - C chord - 5 - C chord. on the 4 beats in a bar. Doubling up, using quavers instead of crotchets, often sounds too busy, and would work better playability wise, in a slower tempo, but that would then make the piece sound too quick. So, improper isn't the word, impractical could be better.
Strumming is often confined to guitar playing, although it could be conceived that playing a chord, specially slightly arpeggiated, may be strumming on piano.