From what I understand about brushes, they are defined by their original shape, so I would say no. That said I would love to be wrong. Brushes are complex tools; possibly themes complex tools PS, so there may well be a way to do what you want.
Are you having issues with particular brush presets, or with everything?
What cursor options are you using in Preferences? I personally like to use Full size, so I know far soft brush presets will spread, and I always have Show Crosshair checked, so I know exactly where I am touching down. This is particularly useful when using the Clone tool, for instance.
What operating system, and version of Photoshop are you using?
Is this issue most apparent with busy backgrounds? I'm guessing this will be a yes. The example below shows the cursor to be more apparent on plain white and black backgrounds, than area filled with noise.
Are you having trouble with the cursor or the paint?