That depends. A (poorly designed) SMPS can easily be damaged by excessively low input voltages, since it will attempt to adjust the duty cycle to stay within regulation. Brownouts can definitely lead to damaged equipment, and 120 V is quite a serious brownout for a 230 V device. Equipment with linear power supplies and heating elements are unlikely to be affected, and neither are pumps I'd suspect. But my main issue is that if you start mixing plugs, it becomes much more likely to plug a 110 V device into a 230 V outlet, something that is likely to lead to damage.
If I were to introduce the complexity of two different mains voltages in my labs, then I would use very different plugs to make them hard to confuse. Plugging things in often happens without thinking or establishing what's connected to the other end of that cord. I'm sure you've occasionally plugged in the wrong cord and noticed the piece of equipment you wanted to power on doesn't turn on. What if this happens with the step-up transformer? I guess you could also use color coding, but using something like a BS 1363 or Schuko plug is an even more obvious way to distinguish.