Vortexing of cells may well damage them, but the amount of damage and the amount of cells damaged by vortexing is very much dependent on the cell type. Certain cells do not mind a short round of vortexing (also dependent on the speed!). We however never vortex cells as our primary cell are quite sensitive to mechanical stress.
a thing you could try is to perform several time point and speeds of vortexing and then continue with a trypan blue staining on an aliquot. This allows you to see the amount of `intact cells` in your solution. Damaged cells will turn blue because the dye is taken up.
As stated before it depends on the cell type your are working with. For instance fibroblasts are insensitive to vortexing meanwhile if you vortex hepatocytes you will have the unpleasant surprise all the cells are dead.
I would generally recommend to use a pipet to pipette the cells up and down to get a more homogeneous suspension, rather than vortexing them, as some cells are more sensitive to being vortexed than others.
It may induce damage on the cells and the amount of damage is dependent on the cell type used. I suggest to use a pipet to homoginize the suspension. But, if do you want to try to use the vortex, you can use an aliquot and successively you could use a trypan blue staining to verify if the cells were alive or dead. Damaged cells will turn blue because the dye is taken up.
I am working with mouse embryonic stem cells. I had issues getting single cells for flow cytometery and I tried vortexing (5-10 seconds) and it worked. I have also subcultured my cells once or twice with vortexing and cells were ok in the following days.