sp_refresh_parameter_encryption fails to refresh objects I am testing always encrypted feature and once the operation of encrypting column is done I have a file with hundreds objects failed to be refresh by the sp_refresh_parameter_encryption procedure.

Should I investigate these errors and perform the refreshing by myself? What are the risks of not doing this?
Generally, you need to check each object this system routine do not refresh. 

It is a good start point to locate routines that are referring the new encrypted columns in not correct way - for example, performing scalar functions on the columns (cast/convert, aggregate, string functions or concatenation, etc.). 

If you do not do this, you risk your application to fail when the encryption is applied on the production database.

It also seems, the engine is not capable of checking/refreshing the CLR routines. In my case, I was completely sure that my CLR objects do not work with encrypted data and just ignored them.