Can you host a server from your machine but use Aternos system of plug-ins and google storage system?

I understand that Aternos does not offer a 24/7 option as far as server hosting goes. I REALLY enjoy the Aternos system as it is user friendly and allowing me to slowly get the hang of Java and what I am doing. Like every other Joe out here I am getting a public server made and NEED it to be 24/7. I have an extra computer I can use to host the server with. I just dont know if that is even a remote possibility? Again, I LOVE how plug ins are plug and play for the most part and love how my google storage is integrated with everything. I guess my question is, can I use Aternos as a middle man user interface to host MY OWN server on my own machine? Sorry if this is confusing! Any help is appreciated!