No, you do want to leave them upright for 2 days so the corks can seal, then store on the sides.
If you lay them down the corks stay wet (from the sanitizer) and if it warms up, they can push right out. Especially since there is some CO2 still in solution.
Wine makers degas the wine in secondary/tertiary so that its dead still in the bottle. I didn't degas well enough and used synthetic corks, and they pushed right back out in a few hours on some bottles.
Primary: English Mild
On tap: Pale Ale, Lancelot's Wheat, English Brown Ale, Steam Beer, HoovNuts IPA
Bottled: MOAM, Braggot, Raspberry Melomel, Merlot, Apfelwein, Pyment, Sweet mead, Cabernet
Gal in 2009: 27, Gal in 2010: 34, Gal in 2011: 13, Gal in 2012: 10