Very doubtful, by my reading of the specifications. The section labeled data transfers does not include DMA, only the much slower interrupts and programmed I/O. The manual referenced change detection but nothing about a timing engine.
Even if you could capture the digital signals, you'd still have to decode it into position information in software. It's much more practical to use a device with a counter that has built-in support for quadrature encoders. It'll be able to handle those signal speeds, and it will do the decoding in hardware, giving you incremental position measurements directly.
NI's X-series multifunction boards would be a good place to start looking.
-Kevin P
CAUTION! New LabVIEW adopters -- it's too late for me, but you *can* save yourself. The new subscription policy for LabVIEW puts NI's hand in your wallet for the rest of your working life. Are you sure you're *that* dedicated to LabVIEW? (Summary of my reasons in this post, part of a voluminous thread of mostly complaints starting here).