For some tests, yes — self-taken swabs and urine samples for STI screening work well at home and are as accurate as clinic-taken samples.
For blood tests we generally prefer a clinic draw. Finger-prick home kits are convenient, but small samples are more prone to haemolysis and contamination, which can produce misleading potassium and other results, and a repeat test undoes any convenience gained.
Where a clinic visit is genuinely difficult, we will discuss the options and be clear about which tests are reliable by finger-prick and which are not.
What we will not do is send you a kit and email you the numbers. Testing without interpretation is where most of the harm in private screening comes from.