Can we use DC-DC Buck convert installed 3.8v battery to power Phone continuously?
It may not be enough, depending on what you are doing on the tablet. It may try to pull more current than just 1.5A. And the tablet may need the battery sensor connection, as its not just power and ground. Some devices are finicky about that (for example, a Mifi 7700 hotspot).

You can certainly try it to see if it will run or not.