Can I perform OR searches in MIRC for Cases?

Under some circumstances.

The most common request for this feature involves the ability to produce a report listing all matters or clients who either owe money or have unbilled activity.

All you have to do is create your report including whatever A/R columns in which you are interested (fees, hard costs, soft costs, retainer, just the total...) for the ages you want (requested by dates of billing or days old) and the unbilled columns (again, fees, costs, total, etc).

In the Table of System Options there is a question that lets you exclude a line of all zeroes in MIRC for Cases. It's under miscellaneous. It's probably already checked, since that's its default setting. If it isn't checked, check it.

If a client owes you something or has an unbilled amount, he will be listed on the report. Otherwise he won't.