In the event it drain is clogged, that definitely qualifies being a home repair emergency. Most of the time, you cannot even use the sink or shower owed to the clogged drain, when the blockages severe enough. You need to get it taken care of right away.
There is also the possibility that, by leaving whatever is clogging the drain within the pipe for an long time, you are making the situation worse. The blockage could harden and be much more difficult to break or do away with. Additionally, depending on just what the blockage is comprised of, materials could actually be damaging the pipes in your home the longer that they sit within.
No, the best decision is definitely to call in an emergency drain clearing plumbing company to take care of the situation when you notice that it is a problem. Although it may seem like a somewhat extravagant expense, it will save money in the long run by taking care of the issue before now you have an even larger issue, where permanent problems for your pipes and overall plumbing system may have become part of the equation at that point.