No it won't. You are licensed for 3 computers. Effectively you have uninstalled and reinstalled it on the same computer so will have it for this and two others. If you do however experience activating the third license, there will always be the option to activate via phone. Here you can speak to a Microsoft representative, explain your situation and who will help you activate.
I installed Microsoft Office 2010 Home and student on my dell laptop. Then after 4 years, my laptop had too much clutter on it so, i resetted the computer back to its factory state using datasafe. If i reinstall home and student again on my dell laptop, will it use another product key activation because my product key with the dvd installation has only one left product activation.
Microsoft 2010 Student And Home Activation Question