No. And if you want to retain vector data then there is no solution. AE only deals with pixels. You will have to render an image sequence or video clip.
I know this is an age old question -- but why can't we do this?! Yes, AE "deals" with pixels in the sense that it renders to them. But it also "deals" with vectors, because it can read and create them. It just seems silly that there just isn't a way to export vectors from AE. I just can't imagine a group of Adobe engineers sitting around stumped by this -- the program has vector data -- why can't we get the vector data out of it?!!? Is copying and pasting individual paths to Illustrator seriously the only way to do this?!
There is one way...
This Movin bodymovin thing purports to get SVG from AE. I've never tried it, so I don't vouch for it, but it looks cool.
It would be nice for AE to have this sort of functionality natively. It'd be an excellent feature request, for sure. Feature Request/Bug Report Form
If Adobe is going to use SVG to move assets around the CC Library, demo them in use at Adobe Max, etc. they should make it a bit easier to get them reliably out of their software. Illustrator users have been having a hard time with it and, other than this, I don't know of a way to do it from AE either.
I was hoping bodymovin would be the answer as well, but unfortunately it does nothing even remotely close to this.
We need this adobe... pixels are for cavemen.