The Global Cooldown is not affected by CDR however usually a bit of CDR can be really useful on Udyr.
The main reason behind this is the stance switching. You can for example use your Q and then quickly switch to Phoenix stance. Like this you can attack faster and thus proc your Phoenix passive faster and also for a longer time or at least more sustained. There are of course also diffenent combos like Q->E for high er sustain. The more CDR you have the longer you are able to keep the Attackspeed from Q on the Turtle passive, the higher your sustain will be obviously.
Generally you should buy CDR but it shouldn't be your highest priority stat. Defensive stats or Attackspeed are more important for example. Your goal should be between 20 and 30% CDR since this allows you to keep a good uptime in a 2 Spell Rotation while not wasting too much money and slots on useless CDR items.