please understand that the following is written with absolutely NO OFFENSE intended ... but you've asked a question – I'll assume that you desire an answer ...
to get the "right" answer, we need to break your question down ...
actually an OTE instruction NEVER receives a ONE ... what you should have said was: "when the OTE instruction receives TRUE logic" ...
going further, when the OTE instruction receives TRUE logic, the processor will go and write a ONE into bit/box B3:13/4 ...
a better way to express this operation is that the rung remains "sealed in" ...
the term "latched" should (ideally) be reserved for the retentive instructions OTL (Output Latch) and OTU (Output Unlatch) ... the reason is that a truly "latched" rung will RETAIN its ON status after a "processor-go-to-run" event ... a "sealed-in" rung (like the one you've shown) will automatically be turned OFF each time the processor starts up ...
the XIC instruction doesn't "become a 1" ... a better way of expressing this would be to say: "since the XIC instruction for B3:13/4 will be evaluated as TRUE" ...
and getting down-right nit-picky about it (again, with no offense intended), you've used the wrong syntax for the address of bit/box B3:13/4 ... and furthermore, your use of "it's" as a possessive is grammatically incorrect ... "its" is the proper form of a possessive pronoun ... "it's" is actually a contraction – for the two words "it is" ...
now back to your original "crazy" question:
suppose that you had phrased the question this way instead:
I respectfully submit, with absolutely NO offense intended, that the only reason your original question was "crazy" (that's your word, not mine) is because you do not know exactly how your Allen-Bradley processor operates "under the hood" ... trust me, you are NOT alone in that situation ...
so ... finally ...
the answer to the properly phrased question would be:
yes, the rung will stay sealed-in – until/unless something writes a ZERO into bit/box B3:13/4 ... or ... until the processor has a "go to run" event – in which case PRE-SCAN would execute the OTE instruction – and cause the processor to go write a ZERO into bit/box B3:13/4 – and so the rung would lose its "sealed-in" condition ...