How can I power a circuit while charging its Li-ion battery pack?
For applications like this better choice is charger chip with power path, something like BQ2403x, BQ2407x etc.

You are correct that this setup will change charging profile, potentially causing charger overheating, undercharged battery or reduced battery lifetime. Or as simple as device not working if charger cannot supply enough power.

If you want to use these components somewhat better solution would be to create additional path from voltage regulator to the load using diodes or mosfets. Check this application note form Microchip for many good ideas.