Yes, and this is how the standard of care treats things. You never proceed from positive mammo screen to treatment. You always first do some other steps like ultrasound or biopsy.
This is the general argument against testing for prostate cancer in non-symptomatic patients. If you only test patients that has symptoms then the rate of false positives goes down. The downside is that you only catch late stage patients where treatment might be too late. The alternative (which is used for mammography) is that for every person saved, an order of magnitude more will be permanent harmed by unnecessary surgery.
It's also why breast cancer screening is not recommended for everyone, just women over 50.
For women over 50 there has been a decades long sincere effort by the medical community to take this all into account and the consensus is that screening makes sense in that population.