I would like to know if I can charge the device at the same time as using the HDMI connection
Theoretically yes but practically wouldn't help {see edit below)
Further, it says
MHL passive cable
Passive cables allow consumers to connect an MHL-enabled device directly to an MHL TV and do not require external power. Unlike older MHL adapters and cables, the passive cable simultaneously charges the cell phone battery while mirroring.
A typical mobile battery charging (without using fast charging) for a capacity of 3000 mAh requires around 1800 mAh
Galaxy Tab S2 has a battery that is either 4000/5870 mAh (depending on the model), which is much more than a normal cell, and it would take real long to charge. It would take 10 / 14 hours respectively (To estimate charging time required , use the Battery Charge Time Calculator)
Note: This is based only on the power calculations part of it. I haven't used MHL / HDMI
Edit: With reference to your comment, if the screen is in use, the power it would draw in all likelihood would be more than charging, so in effect, it wouldn't help at all. See this answer to get an idea of power used in screen on condition