Sadly, No. The East River MUP doesn't exist in that part of town. It takes a rather long detour around the UN and Sutton Place, you have to use either 1st or 2nd depending on whether you're heading up or downtown. There was at one time an entrance around 62nd? heading uptown but there is a lot of construction for the FDR in that area at the moment. And as I haven't been training for the Marathon in a couple years, I'm a bit out of touch with the part of the MUP that runs from the Queensboro to the Triboro.
I do ride southern portion down to the Seaport from the Queensboro several times a week, and can tell you that it's not all that pleasant from 34th to 23rd either, they didn't plan it very well to get around the Waterside Plaza apartments and the Water Club, you have to merge in with the tunnel traffic coming off the FDR.
That said, once you actually get on the MUP, it's a really nice ride/run/walk whether you're south of 23rd or north of the 60s, more than worthly of the hassle of the crazy bits in the middle.