nohup mode has no relevance on whether the process is I/O bound. So yes, slow storage will probably slow down the process.
If the process has bursty output (e.g. 10 lines every 1 hour), but throughput lower than your "slow" storage, then you can improve performance by e.g. writing to a pipe or a FIFO (which then gets copied to the slow storage by another process), as long as one burst of output doesn't exceed the pipe's buffer.
nohup prog >/tmp/fifo &
cat </tmp/fifo >slow_log_file &
nohup prog | buffer -s 16k >slow_log_file &
where buffer is a special program (available on Debian with
apt-get install buffer) that maintains a large internal queue to avoid blocking the writer.
Or if you control the source code, you could implement buffering yourself and maybe use a separate logger process to write to the slow storage. I know djbdns (famous for its stability) uses a logger process.