Does succumbing to a disease or poison using the pathfinder unchained disease rules make you incapable of receiving a raise dead or similar spell?
From what I can tell no.
A raised creature has a number of hit points equal to its current HD. Any ability scores damaged to 0 are raised to 1. Normal poison and normal disease are cured in the process of raising the subject, but magical diseases and curses are not undone.
Usually, neutralize poison or remove disease immediately moves the victim to a healthy state on the respective track, and a heal spell will work for both. However, once the disease or poison has reached its end state, only a more powerful spell such as miracle or wish can remove its effects.
Raise dead is not miracle or wish so does that mean a character that succumbs to say filth fever is dead forever until they can gain access to a wish spell?
That appears to be the Case RAW, which seems very harsh.
I would assume Reincarnate is the only way around this as it creates a new body (thus circumvents all physical afflictions)
Also does a disease continue to 'tick' even when the host is dead? I.e if a character dies with filth fever on them does the corpse continue to 'save' and thus move down the track (possibly preventing Resurrection)?
Specific trumps general. If raise dead removes normal diseases, it removes normal diseases, even if the unchained disease calls out stronger spells. And Raise Dead is a stronger spell. That part in diseases was rather unclear.
Heal is more powerful than raise dead, and Heal is called out as not working. Which would imply 7th level spell or higher minimum (although explicitly 9th level is required). Which means Resurrection should be sufficient by that reasoning.
Given that Resurrection has the ability to totally restore a body (remains are not an issue) it would seem that it would remove the condition by virtue of that function.