Yes harmonics issues are possible if using cheap PSU's. However, most today have PFC - Power Factor Control - that mitigate the problem. Most will advertise if they have PFC and give a Power Factor rating. A perfect resistive load gives a PF of 1.0 and most PSU's will be around 0.85 to 0.9
^ This.
More usual case to end up in problems with harmonics is that if you have a lot of load consisting frequency converter controlled electrical motors for example.
So if you use good PSUs with PFC inside, harmonics shouldn't be an issue.