Three-way charge?

Can I have my MagSafe battery pack attached to a power source while attached to my iPhone, and simultaneously having my iPhone attached to another power source and charge both battery pack and iPhone at the same time? I understand the MagSafe battery pack can be reversed charged with the iPhone attached to a power source but my question is, can I do that without the reverse charge and instead I have both MagSafe and iPhone attached to a power source while simultaneously attached to each other?

for instants, my battery pack is fully charged, but my iPhone isn’t so I plug in my iPhone as well as my battery pack while my battery pack is attached to my phone will my iPhone charge quicker or will it charge the same as just one source of power via lightning cable would?