Aquarium chemistry

I set up a small aquarium and used de-chlor. Waited a week and bought a
goldfish. After one week it had Ich, used malachite green and raised tank
temperature to 80 deg., it recovered. Then at it's 2 week mark the goldfish
looked ill and had its tail corroding - I assumed with tailrot. Took a
water sample to a petstore and wanted to buy an anti-biotic. The aquariaist
said that the sample had high ammonia and that it was not tailrot, would
not sell the antibiotic. The fish died that night.

http://fins.actwin.com/mirror/begin-cycling.html

My question is - with no fish in the tank to continue producing nitrogen,
will the cycle shown in the graph on the link above continue as depicted?
Or will the cycle be interrupted until I install a new fish to produce new
nitrogen? My preference would be to leave the tank alone until day 40 and
then feel much better about putting in a new fish.

Could not find a group where this would be on-topic, but it is related.