Does this huge collective quantity of objects (together with space trash) reflect away enough solar radiation to have a measurable effect? Could this affect Earth's climate, mitigating climate change?
Suppose, instead of 12,000 tiny satellites, SpaceX was planning on launching 12,000 satellites the size of the International Space Station. The ISS, with its huge solar arrays, has a cross section of about 7,000 square meters (6,528 square meters for the arrays alone). Fun fact: This is about the size of a FIFA-sanctioned international match field. I'll bump up the size to 8250 square meters, the maximum size of a FIFA-sanctioned international match field.
The ISS blocks sunlight that would otherwise hit the Earth about half of the time. I'll halve the 12,000 satellites to 6,000 to reflect this. Six thousand maximum-sized FIFA-sanctioned international match fields results in an area of 49.5 square kilometers. The Earth's cross section to sunlight is $\pi r^2$, where $r$ is the Earth's mean radius (6371 km). This cross section area is $1.275\times10^8$ square kilometers. That's over 2.5 million times larger than those 6000 maximum-sized FIFA-sanctioned international match fields.
Summary: Even 12,000 satellites larger than the ISS would have a minimal impact on the amount of sunlight hitting the Earth. The 12,000 satellites SpaceX is planning to launch are orders of magnitude smaller than the ISS. The impact is in the noise.