You should use RT or a RDC to check the DT and determine the answer yourself. I strongly suspect that the overall DT of the bed will be higher than what you would normally want. But the answer would also be gauge dependent as well as selected ref tension. So let's assume a simple 16 Ga SG case.
When crosses are tensioned, they have to fight against string friction from the mains AND the tension in the mains that want to keep the mains straight. You can remove a lot of string friction by moving the cross as it is tensioned. You cannot affect the issue created by the tension in the mains. They help your crosses achieve ref tension by pushing back.
By raising the mains out of the way, the crosses will be tensioned at ref tension without interference from string friction AND tension in mains. But when the tool is removed, the mains will have to come back to equilibrium by pushing the tension in the crosses higher or by increasing the tension within themselves. Each time you use the tool, it will increase the tension in the strings as the artificial displacement is removed.
You can argue that the tension difference is not significant since in both cases, the mains have to reestablish equilibrium. I would not be able to refute that. Only way to really know is to compare the DT or ref tension of the string bed in both cases.