Yeah, it's definitely possible.

: Also, Emmy and I had no connection problems with Reach. Is it possible that
: it was just Halo 4's servers that were not allowing us to connect?

It's absolutely possible, but as KP said that probably would have been noticed (if they have anything close to decent monitoring, it would be clear when the number of connected players suddenly drops to abnormal levels), and typically MS acknowledges it when there's a widespread outage.

It's also worth noting that the internet is made up of many individual links, from one company, to another, to another. One of them could have been having a little trouble - the possible list of culprits extends to more than just the players/their ISPs or MS. This is why KP was talking about ops tracking major outages that would affect the service - no doubt they keep an eye on neighboring networks which large numbers of connecting players would be routed through. A problem could develop between you and MS without it being the fault of either you or them (but the XBL folks probably would have known about if it was widespread) or even between you and other players (which XBL may not necessarily know about).

It's also possible that what you and other players saw as a distinct outage was in fact a bunch of small hiccups, not actually related but just coincidentally occurring around the same time. Without any hard data it's hard to say.