Not necessarily, but it is possible; and it’s likely if the OCD goes untreated.
The course of OCD is not 100 percent predictable, so it is impossible to say for sure whether OCD rituals will morph into other areas.
If OCD were to spread, it would most likely be in the same theme though, such as the checking mentioned in the question. Checking a door and checking a window can be easily related to each other, whereas checking a door and then hoarding all of your newspapers are not related to each other.
This type of migration would be less likely to occur.