So they probably would have obtained the ATC tapes. Ukraine is part of the investigation team, so they wold have taken the ATC tapes with them, I assume. It is not likely to show anything relevant, except perhaps settle the conspiracy about MH17 being deliberately vectored into a trap.
The Dutch Minister of Foreign Affairs Frans Timmermans has replied to parliamentary questions stating that there was no horizontal deviation from the route of MH017. The only change to the flight plan was a descent from 11 km (FL350) to 10 km (FL330) ordered by Dnepropetrovsk ATC in order to avoid a conflict with another aircraft at 11km (FL350).
Original text in Dutch (question 7e) is to be found:
Lijst van vragen, brieven ?Repatriėringsmissie MH17? en ?Stand van Zaken vliegramp MH17? | Kamerstuk | Rijksoverheid.nl
One element of conspiracy theories countered indeed.
On the other hand, the full CVR conversation may not be published, which will undoubtedly give room to other conspriracy theories.