I was a little bit stunned by your description of tendinopathy. So I just had a look at the internet to be sure I am not going to write complete nonsense. (Just go on google or to med-line to look it up).
OK, according to my latin knowledge, which is sparse, Tendino-pathy means disease of the tendon and is none specific terminology alike lumbago. It is caused in general by overuse (short term/long term) and it has implications for the build up of the tendon, crosslinks name it. A reaction to the condition will be an increase of bloodvessels and likely an increase of nerve endings. This is a common response to injury. Tendinopathy has not necessarily as a symptom inflamation and more often not than it will have.
The use of ice has no influence on the inflamation since most likely it is not a problem. But a complete other effect of ice is pain control. an effect directly on nerve endings, look up which, which will decrease and normalise their firing speed.
You ask if ice would not decrease the bloodflow and decrease the nerve endings. Well Ice does increase bloodflow, but this is arguable, but will for sure within an application of 10-15 minutes have no effect on the amount of nerve endings.
To my opinion yes you can use ice and it could well be very beneficial. aside of stretching (rupturing crosslinks), strengthening synergist (off loading). But what about restoring balance between e.g. extensors and flexors?
Keep in mind that tendinopathy is just a general terminology which doesn't tell you anything about it's cause. which might have been poor bloodsupply in the first place!