Short answer: you should never buy Guinsoo's Rageblade or BoTRK if you want to tryhard and win games consistently.

Long answer: it is simply not viable to buy such expensive and solely damage-oriented items. Udyr has more than enough damage to make do with in the early and mid game. What he could always use more of is utility and tankiness. Very, very exceptional cases would be games when you are matched against three or more heavy tanks and often find yourself fighting long skirmishes, when you could go with a Rageblade. Such games are practically nonexistent in the current meta, though. You could go with a BOtRK in lower elo games - just for the fun of it, but it is still simply not viable.

That is why you take Rejuvernation Bead as a starting item, which costs 150 and builds into tiamat!

Yes, definitely! I just added a whole chapter on that in the guide.

I personally do not consider it viable as this build revolves around popping up and bursting down enemies, so you will find that you rarely actually get to stay in combat long enough to benefit from Conqueror. You could try to make it work, but if you want to go with conqueror I would recommend going for a tankier build, and getting red smite Cinderhulk as a jungle item.