It certainly can. Ink will dry in the print heads and the cleaning process will be unable to remove the dried ink. If the printer is properly turned off using the power switch on the printer, the capping assembly will cover the print head and slow the process so it can take a while to have a negative result.
You can sometimes have no issue after an extended period of non-use but if three-four cleaning cycles does not give a good result, it will need professional attention or at least the use of a proper cleaning solution. That can work but care is needed.