Can you see further when diving with a flashlight in cloudy water?

Depends on how dark it is down there and how cloudy the water is. Sediment in the water column attenuates the light, so you need to bring your own lighting.

Obviously if the sediment is soup like, such as if someone's fin has kicked up the bottom sediment, there's not much that a torch can help with.

If it's just a bit mucky, e.g. following a storm or an algal bloom, then a torch will help cut through the sediment. You will find that a bright and tightly focussed torch beam (say 6 degrees) will be much better than a wide beam which creates a lot of back-scatter. Also a bit of an angle between you and the beam can help too, holding the torch out to the side.

If the sediment's been kicked up you may find some better visibility if you gently ascend a little.

A "Goodman Handle" on the torch helps to hold it whilst leaving your fingers free to grip things, such as a reel which you may use to 'line off' off the shot line/anchor.

As a diver of 30 years now I doubt you will derive much benefit from using a run of the mill torch in cloudy water. Using a torch means giving up one of your hands so when it comes time to feel around on the bottom you will be very restricted and clumsy doing it with one hand and you will get unbalanced. You won't forget where the surface is, as you will naturally float upwards, but you may find yourself under an obstruction that may very well cause you to panic and drown