Deployed Web service
In training set:

You would better use some methods to "presume" certain values...average / pro-rata......which you could find in various learning sources

Leaving them as blank (not sure of Azure but in a low level programming platform) would cause either inaccuracy or problems.

For testing set:

You are not changing the Learned Parameters, but still that would probably causing some inaccurate measurement but Azure ML may have done something internally.

Reference from MSDN:


  How to deal with missing values?
  
  To deal with missing values, it is best to first identify the reason for the missing values to better handle the problem. Typical missing value handling methods are:
  
  
  Deletion: Remove records with missing values
  Dummy substitution: Replace missing values with a dummy value: e.g, unknown for categorical or 0 for numerical values.
  Mean substitution: If the missing data is numerical, replace the missing values with the mean.
  Frequent substitution: If the missing data is categorical, replace the missing values with the most frequent item
  Regression substitution: Use a regression method to replace missing values with regressed values.