*Technically* you can play along to music in any key with a single harmonica IF you're able to play your harmonica chromatically (You'll need to be able to bend, overblow and overdraw all your notes on the harmonica - which only a handful of player worldwide can do with proficiency – google Howard Levy, he is known for mostly playing a C in all 12 keys).
With regards to your question, yes you can play along to music in E on a C harmonica, you'll just have to play in 5th position/Phrygian. The problem is 5th position just doesn't sound as bluesy as 2nd, because your root note is on a blow note, and blow notes just don't sound bluesy, because you can't wail on them or manipulate them like a draw note. 5th position works for minor stuff, but you've got to watch out for which notes you resolve to, cause it may sound slightly off.
Playing 5th position your lower octave pentatonic scale will look like this:
(the minus sign indicates a draw note. The ' indicates a bend: ' - semi tone '' - whole tone ''' - 3 semi tone bend)
2 -2 -3" -3 -4 5
Now that 3 draw whole step bend is particularly difficult to hit consistently.
The problem is that you can't hit the 3 draw unbent and bend into it and you can't bend past it either. You've gotta be able to hit the 3 draw whole step bend on its own... and that take practicing (and is very difficult without a harp that's gapped nicely). Ignore that bit... 3 draw on it's own is part of the scale. Hitting the bend is slightly easier when you can bend into it, but proper intonation on all the 3 draw bends takes a while to get right!
Playing on the second octave is bit difficult because it starts on the 5 hole, but the reeds flip from the 7th hole, meaning that 7 - 10 blow are actually doing the bending... so you can't lower the 7hole b to a bflat. See how the notes flip from 7 onwards (Grey notes are overbends)?
So back to your question on why an A harp is more suited to blues in E. It's because 2nd position is just sounds more bluesy and it's much easier to play it and get it sounding nice and bluesy.
Have a listen to Richard Sleigh playing some 5th position. You'll note his harmonica playing doesn't sound particularly bluesy, but it's got a distinctive minor sound.
