Another neat trick to quiet noisy lifters is to use special oil additives to reduce lifter noise. This is another one which is aimed at those with noisy hydraulic tappets rather than solid ones. There are a few companies who have developed additives specifically formulated to reduce noisy lifters.
How do you stop a valve lifter from making noise?
What causes lifters to tick?
A lifter tick is caused when the push rod or camshaft doesn't make continuous contact with the lifters. This can be because the lifter has become worn out, as is the case usually with hydraulic lifters, or the valve has come out of adjustment.
How do you free up a hydraulic lifter?
Run an engine detergent in your gasoline, and use a higher-octane gas. Often, fuel system cleaners or detergents can free up engine debris and stop a valve lifter from ticking. Use an engine flush, and then change your oil.
Related Question how to quiet noisy lifters
Can you drive a vehicle with a collapsed lifter?
Now to answer the original question you should be fine running your engine even if the lifter is collapsed.