Unfortunately yes. It'll overheat and start to melt the connector. Either the fan motor itself will burn out or the plastic connector will start to melt allowing the metal pins inside to start making false contact and the fan will stop running. Now you have two speeds on the fan. I've never tried running it on low speed only. This may save the fan but would probably cause overheating on real hot days with the ac on.
What I did in my car is wire it straight on high speed. I control it through a switch on my center console. On the highway I leave it off cause it's not needed. I turn it on when in the city. Of coarse having it wired this way requires me to keep an eye on the temp but I'm used to that anyways.