The short answer is No. In order for mSATA to be supported, a SATA lane needs to be routed to the mPCIe connector. Since the single mPCIe connector on TY was expressly intended for the support of a WiFi/BT module, no SATA lane was routed to it.
I suppose (though I have never seen one) that there is the possibility of a mPCIe SSD that includes its own PCIe SATA controller. Whether such a product would fit on the board is a question (it would need to be half-length (25mm)).
All this said, there is an alternative way to connect a mSATA SSD to the TY board. You can purchase adapters that allow a mSATA SSD to be connected to a SATA interface. Here is a link to one such adapter: Amazon.com: mSATA to SATA Adapter. I have purchased a couple of these type of adapters myself - including this specific one - and have used them to connect mSATA SSDs to multiple NUCs, including TY. Here's another example if physical size of the adapter is an issue: Amazon.com: mSATA to SATA adapter (I haven't used this specific one, however).
Hope this helps,