Not really, no. Not to the same extent as "West Coast Drive", which is fairly common, popular, and has many ubiquitous elements. (Cantilevered wheels, rectangular tube, a direct driven wheel, etc)
The closest thing there would be to an "East Coast Drive" would be a drive similar to the style used by teams like 11 and 125 - 1/4"ish aluminum plate, usually lightened, held together with standoffs. Non cantilevered wheels, sometimes dead axles in order to take advantage of the "free" standoff these axles become, and often not direct drive. Chain reductions between the gearbox and the wheels are common.
This isn't a thing anyone really calls an "East Coast Drive" except in a tongue-in-cheek manner, though, and it's certainly not as popular. It's difficult to design an "east coast drive" that is as light, rigid, and easy to manufacture as a WCD, but as with all design decisions in FRC it comes down to what works best for your team.
On a related note, my team (2791) made an "east coast drive" in 2010. Without much experience, we were unable to make this drivetrain as light or as rigid as it should have been, and we have had a much easier / better time with our WCDs since then.
