In theory, yes, stapled OCSP should mean that your server can continue to serve a stapled response up to ~7 days (the lifetime of the OCSP response), and be robust to OCSP responder outages. In practice, however, there are a couple of factors that interfere. The main one is that when browsers make their own OCSP requests, they generally "fail open" if the responder is down, and no one noticed. But Firefox intentionally treats stapled OCSP more strictly, because they are trying to prepare for a world where Must-Staple is more common. So if a responder is serving bad responses, and the web server staples them, Firefox will show certificate errors, even if it wouldn't have shown those certificate errors getting the same bad response from the OCSP responder directly.
Web servers could mitigate this by caching OCSP responses long-term and not updating the cache until they get a good response from the OCSP server. This would mean that outages shorter than a few days could be weathered nicely by those servers. However, the most popular servers don't do this.