Well, it's a matter of secrecy. To be a Heroic Spirit, you have to be known about, and Shiki isn't. I think it is unlikely that Shirou would become well-known enough to do it, but not necessarily impossible (if some sort of big magical war were to happen, for example). And, as Lantz has pointed out previously, if something is possible, however unlikely, then the fact that the Nasuverse is a Multiverse means that it probably has happened somewhere.
I'm not saying that Shirou has become a HS somewhere, but I don't think we can absolutely 100% rule it out. It's just not something that is likely to happen very often if at all.