Though you can pray in any position, physical position does matter.
On the subject of why it might matter a monk wrote:
Be conscious of physical position as well as soul During prayer
one should stand straight with ones eyes fixed on the icon or lowered
to the ground, while, at the same time, the eyes of the soul, together
with one's soulful aspirations, should be lifted up to God. This
outward attitude of piety in prayer is both necessary and beneficial,
for the disposition of the soul is in conformity with the
disposition of the body.
(Eastern Christians pray in front of icons, usually.)
To further the point, kneeling and clasping hands, as well as standing upright seem to be try to achieve the same thing; matching the proper disposition of soul with that of body, with the idea in mind that they are connected.
If you wished to beseech, say, your best friend to help you, what position would you speak to them in? And what about someone far greater than they? This is the reasoning behind selecting a physical position, whether it be standing up straight or kneeling reverently.
The final point is that it is considered that the position of the body will affect the disposition of the soul, and thus while it is better to pray than to not pray, it is better to pray in a position which reflects the disposition you'd wish your soul to have.
- Standing upright reflects alertness, vigilance, readiness
- Kneeling reflects devotion, reverence, acceptance
To conclude I would say there is nothing wrong with praying supine, but that your position will affect the way you pray, and that there may be a better way.