You could threaten the ground-based over-the-horizon radars, but the loss of space entirely would not have a major effect on them because they're primarily interested in air-breathing threats. You have, on the margin, the question of hypersonics, which fly at roughly 50 kilometres an hour in what I call suborbital space—at high speeds. It's unclear to me whether the over-the-horizon system—and it would need to be cued to look at things—would be significantly affected. It's unclear whether the over-the-horizon radar can actually look.
The other thing I would add is that the United States has deployed an infrared system in low-earth orbit to deal with the problem of ballistic missile defence and, I suspect, the problem of hypersonic vehicles. That's another degree of redundancy for the American space surveillance system.