Sure it can. It just won't be able to learn Roost, and it will be the only pure-Flying. Though I'm not sure about what happens when you are brought down to the ground with Iron Ball or Gravity...
Aeoleon was supposed to be a Cloud-form Eevee.
I suppose you want me to make a Rock-type Eevee then, since the other one was Ground / Rock, with more Ground-type characteristics.
Eroseon or Boldereon/Buldereon or Stoneon
Rock
Iron Head
-- Tackle
-- Tail Whip
-- Helping Hand
08 Sand Attack
15 Take Down
22 Quick Attack
29 Bite
36 Sharpen
43 Stealth Rock
50 Last Resort
57 Sandstorm
64 Rock Polish
71 Head Smash
I'm going to change some attacks for Litheon:
Litheon
Ground
Rough Skin
-- Tackle
-- Tail Whip
-- Helping Hand
08 Sand Attack
15 Sand Tomb
22 Quick Attack
29 Bite
36 Magnitude
43 Lock-on
50 Last Resort
57 Mud Bomb
64 Spikes
71 Fissure