The Wikipedia entry you linked and the other answer both state that...
... the systemic heart is inactive while the animal is swimming and thus it tires quickly and prefers to crawl.
I tried to find an accurate source corroborating this (by accurate I mean a paper in a peer-reviewed journal or a zoology book), but I couldn't. The best source (scientifically speaking) I found was this page from the Smithsonian Institute, which says:
Octopuses have three hearts. Two of the hearts work exclusively to move blood beyond the animal’s gills, while the third keeps circulation flowing for the organs. The organ heart actually stops beating when the octopus swims, explaining the species’ penchant for crawling rather than swimming, which exhausts them.
A much more reputable source is Octopus: Physiology and Behaviour of an Advanced Invertebrate. It says:
If an octopus is surprised by a sudden movement on the part of an observer, or a thump on the side of its tank, the systemic hear may miss one or more beats.
Which is, evidently, way less dramatic than having one of the three hearts stopping.
The same author says, talking about Octopus vulgaris:
Together with changes due to exercise and arrests attributable to sudden tensing of the body musculature, any prolonged recording reveals apparently spontaneous changes in amplitude that are not obviously correlated with anything that the animal can be seen to be doing. From time to time the heart stops for several seconds (as it does, for longer periods, in O. dofleini).
Thus, apparently, the maximum we have here is periods longer than several seconds (which the book, unfortunately, doesn't determine more precisely).
In conclusion, despite their circulatory system being very complex and the systemic heart being able to stop beating for several seconds (or during the whole time of swimming, as the Smithsonian says), it doesn't seem possible that octopuses can survive if one of their hearts stops (forever). Have in mind that the hearts are not redundant, that is, one heart cannot perform the function of the other (if that other one stops).
Source: Wells, M. (2013). Octopus. 1st ed. [Place of publication not identified]: Springer.