Yes, a limitation of the Friedman test and ANY test with blocking is that the blocking variable does not interact with the factor.
To expand on this, suppose you have 10 blocks and 3 treatments. With the Friedman approach you are calculating ranks within each block. The ranks within each block will always add to 6. Therefore, when you conduct the testing there will not be any difference between the blocks (sums of squares will be 0 for the block effect).
If you DID put in an interaction (which you could try within JMP, you just need to use Fit Model instead of Fit Y by X), you would have 9 DF for the blocks, 2 DF for the treatment, and 18 DF for the interaction. You have 0 DF left for error. You have a saturated model and no testing would be available.