I use the UA website to check for availability. While I have an active UA FF account, one can search for availability without being member of UA MP. With NH you need to sign up first and IIRC NH now requires to have miles on your account in order to search for award flights.
On United.com enter your desired route and click on "Award Travel".
UA has two columns for every class of service.
"Standard Award" and "Saver Award".
Availability in the "Saver Award" column for your desired class of travel should translate into available Star Alliance redemption seats visible to TK.
There is no guarantee that the flights you searched for will be available through TK M&S. While I am not aware of TK blocking certain airlines, some airlines might not release all award inventory to TK.
LH Group premium cabins spring to mind.