Heavy equipment can easily destroy the tiles in your drain field, it they are similar to the perforated plastic tubes my drain field has. But that term heavy equipment does not apply to your mower or a rotor tiller of normal size. A farm tractor would be heavy equipment, however.
Clover could grow there and would be acceptable providing the soil meets the needs of that clover, a proper soil pH range (6.2 to 6.8), sufficient levels of nutrients to support good healthy growth and good drainage, but an evenly moist soil.
Contact your local state universities USDA Cooperative Extension office about having a good, reliable soil test done before going further to see what needs be done with your soil so the clover will grow and out compete those weeds.

Some people plant a mix of prairie wildflowers and grasses over their septic system.

There are seed mixes designed specifically for this purpose.

Here is a link that might be useful: septic prairie mix