No it will not ... the reason for the limit is to stop the use of one program by multiple unrelated people. If all you had to do is uninstall it one one computer to put it on another one then what is the use of limits?
If anyone needs to file a return and you will not let them on your computer then they should use the IRS FREE FILE option instead ... if their AGI is $69K or less there is a program for them here : https://www.irs.gov/filing/free-file-do-your-federal-taxes-for-free
