According to the HTTP spec, the request-target token can have multiple values "derived" from a URI path. From the URI spec a path can only contain printable 7-bit ASCII alphanumeric characters and a few symbols like '-', '.', '%', '~' and others. It does not allow ASCII control characters.
According to the URI spec, path characters outside the printable 7-bit ASCII range should be percent-encoded, so ASCII DEL should be encoded %7F and ASCII NULL %00.
It's hard to say whether percent-encoding your binary characters “would work” as you do not explain what you expect to get from them. An HTTP request-target is an opaque identifier interpreted by the server, and need not correspond to a file name or actual data. It is perfectly feasible (and common) to refer to binary targets with ASCII alphanumeric request-targets.