That depends on how harmful the screening is, how harmful treatment is, how harmful the disease is, how well the test works, and how common the disease is. (probably more that I'm not aware of)

Most cancer treatments are really nasty. Thus false positives are really bad: you destroy someone's quality of life. The earlier cancer is discovered the better chance that we can use a less harmful treatment (if only because of smaller dose of the harmful drugs)

The current breast cancer screening is an xray - which itself causes cancer (about 1 in 3000 cases of breast cancer discovered by xray wouldn't have got breast cancer in the first place without the screening - the screening is still wroth doing if you are at risk, but don't do it if you are not at risk).

Breast cancer can be deadly, but if caught early it is easy to treat (normally).

The medical concern generally isn't should we test all women for breast cancer, but when do we start testing and how often should we test. If this test is safer than an xray and sensitive enough it can be useful. Avoiding current breast cancer tests is good.