Informing Court of non-probate assets?

As a general rule, the answer is no. The court has jurisdiction to determine the distribution of asset subject to probate only. If a decedent dies with assets that are going to distributed pursuant to contract (for example, life insurance, annuities, or IRAs), or a jointly-held asset, those will not be subject to probate.

Sometimes those types of assets I described don't have an individual named as beneficiary (or the named individual might have predeceased the decedent), in which case they will pass as part of the decedent's estate, through the probate.

There may be exceptions in your jurisdiction to that general rule, however, and if you are unsure, you should check with someone in your county.