I am not aware of any studies directly measuring this; however some information is available in related studies.
I found the following studies on cholesterol turnover in humans.
- Distribution and turnover of cholesterol in humans
- Cholesterol turnover in human plasma lipoproteins: studies with stable and radioactive isotopes
I found this review of cholesterol lowering therapies. It has some data on vegans under placebo, but none on a vegan diet as treatment.
- The Interpretation of Cholesterol Balance Derived Synthesis Data and Surrogate Noncholesterol Plasma Markers for Cholesterol Synthesis under Lipid Lowering Therapies
Some relevant info
The following graph from 1 shows the lifetime of an injected dose of cholesterol in the body. This might be an indication of how long consumed cholesterol will stay in your body, but can not be taken as an indicator of total cholesterol levels. Total cholesterol levels are also affected by cholesterol synthesis and excretion which is regulated by the body.