This PropertyUtils code from OGNL is written to be thread-safe, and so I would guess that compiled expressions are intended to be thread safe.
Further evidence is that most of the accessor API provide the mutable state as a context parameter (e.g. see PropertyAccessor), so the classes themselves have little mutable state. Immutable classes are intrinsicly thread-safe. The developer guide urges extensions to be thread-safe, and finally
looking through the code, where there is mutable state, it is guarded in a synchronized block, for example see EvaluationPool.
In summary, it seems OGNL has been designed to be thread-safe. Whether it actually is or not is another question! You could write a quick test to see for sure, using for example Concutest. Alternatively, if the number of threads is reasonable, storing all the expressions in a ThreadLocal sidesteps the issue altogether, at the cost of a little extra memory (or possibly not, as OGNL does expression caching.)