Yes, that is correct in this context.
Checking something usually means validating that it meets some specific criteria (e.g., homework answers are right or wrong). Checking on something usually means checking the status of something (e.g., homework has been started or is finished). A similar example:
I need to check the maid's cleaning.
I need to check on the maid.
In the first sentence, you're checking the quality of the work the maid has done. In the second sentence, you're checking on the status of the maid (for example, has she started? is she done?).
I think it's important to note that in these examples, what you're checking and what you're checking on are two different things. There are cases, however, where what you check and what you check on are essentially the same. In that case, you can use either. For example:
I need to check the turkey.
I need to check on the turkey.
In both cases, you are presumably checking to see if the turkey is done so you can eat dinner. Checking the turkey might mean checking its temperature, but that's essentially the same as checking its cooking status.
