Maybe yes, maybe no. It really depends on how the policy is written and the laws and court actions governing your neck of the woods.
Is there an exception in the policy for the unopened street or streets in general? If so, your title insurance likely does not cover it.
Is there an exception in the policy for matters covered on a recorded plan? If so, your title insurance likely does not cover it.
Unopened streets in some areas are abandoned automatically after some time, but in other circumstances they may remain as rights of way available to others.
In any case, if you haven't yet closed and purchased the property, get a clear statement in writing on the issue from your title insurer. Is it covered or not?
If you already own the property and are having some kind of trouble with the unopened street, file a claim with the title insurer in writing. If you've reviewed the policy and find no exceptions and are unsatisfied with the response, contact your state insurance department for assistance.