Despite what people commonly think, not really. A watch is basically a tiny machine created to perform a particular function, which is to measure time. However, in the case of a chronograph, the device becomes more complex. Instead of a single train of wheels, there will be two different and independent ones measuring different quantities.
The remarkable thing about the chronograph, as well as other horological complications, is that this function can be switched on and off at the user's will for their needs but is designed to work reliably when required.
This means that, despite common opinion, it is possible to leave the chronograph function on without incurring any adverse effects on the efficiency of the timepiece. The only results will be increased consumption of the mainspring power, as the mechanism has to drive two trains of wheels and not just one, and increased friction in the inner workings, which causes the watch to need regular overhauls to keep working reliably.
However, what might change things is constantly operating the internal mechanisms, hence the different levers, gears, and wheels, which precisely accentuates this need for lubrication to keep the watch in full working order.
But beyond this, if you happen to leave your chronograph running by accident or by choice, there's no need to despair: your timepiece is made to withstand tests far more demanding than leaving it running.