Only in the late-game. A weaker early game can really impact a champion, especially adc's (who have the weakest early game, hence why they tend to have supports).
Actually, not all ADCs have weak early games to the point of needing a support to survive. Certain ADCs have enough tools to survive (and even thrive) when laning alone. Examples:
- Regularily seen as a mid laner last split. Could build like a bot Corki or more poke oriented.
- Faker's mid Ezreal. 'Nuff said.
- Should, in theory, be able to top lane, especially against melees.
- A common top laner, and also stronger there than bot statistics-wise.
- God, how I hate facing her as a top laner. PTSD.
Basically, for a solo ADC, you'd want someone who can get away from potential ganks and who scales well with XP, in addition to gold (in a lot of pro games, mid laners and sometimes even top laners actually have more CS@10 and @20 than the bot ADC).
The reason ADCs go primarily bot with a support nowadays is rather that, of all possible champion classes, they are the ones most able to share XP with the support. Autoattack damage statting (AD, AS, Crit, ArPen) is set-up in a way that makes purchasing items way better than simply leveling up (a level in a spell = ~60-80 increase in damage, just from the extra level. DPS increase from leveling = ~2-4 points -- you only get about 3 AD/lvl on most ADCs, and base stat-intrinsic AS is only around 1.0@18).