By default, ProConnect does print the estimated tax vouchers as part of the government copy.  However, if you need to change what is printed you can do so by going to Settings --> Print Settings ---> Government Copy --> Federal Estimates --> Check the box for the Federal Estimate Vouchers and the same can be done under State Estimates for the State Estimate Vouchers, as well.  Those settings can be customized for each of the modules where vouchers are applicable for estimated payments, respectively.  If you do not have access to those settings, it would most likely mean that you are not a user with administrative access inside ProConnect and the user with that access can make the changes for you.  

In regards to manual estimated payments and printing, you can choose to print a return rather than utilizing esignature.  Use of Intuit Link for documents is also not required to utilize the software.  Lastly, estimated payments are not required to be made through the software and are only set for electronic payment if you enable that checkbox to do so.  There is no requirement for any parts of the software to be done electronically if you or your client does not want to.