Of course yes, especially with regards to the internal consistency. When you run a test of internal consistency (e.g., Cronbach's alpha), "it describes the extent to which all the items in a test measure the same concept or construct and hence it is connected to the inter-relatedness of the items within the test" (Tavakol and Dennick, 2011, p.1). Therefore, deleting an item would change the whole calculation of your Cronbach's alpha and it might change the acceptability of its internal consistency. The risk is : questions would not be reliable enough to the sub-factor and to the whole phenomenon you try to investigate.
To my opinion, you should previously test your questionnaire with the deleted items.
Here is some references:
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika. 16, 297-334.