Most firms really frown on that type of activity, for a couple of reasons. First, when an attorney employed by a firm represents a client independently from that firm, professional liability concerns are raised. Most firms would prefer that their liability insurance not cover those types of activities, but the fact of the matter is that its not a clear cut question. Second, most firms do not want their associates distracted by clients that are not "firm clients." Third, an associate's representation of "non-firm" clients can lead to conflicts issues that might prevent the firm from taking on business from another client, or another prospective client.
Thus, while some firms may allow moonlighting, there are many, many reasons for them not to object to it.