Originally, our table was situated in the same position as yours. We hated it that way, and I ended up unscrewing the screws, that when through the 4 feet of the table and directly into the floor, and then turned the table 90 degrees up tight in the corner and used only 2 chairs. I screwed it back down in that same position with the same screws.
If you reposition the table and use the same screws, they will not extend any farther into the floor than they do right now. Yes, you can move the table.
We eventually removed all the screws and left the table 100% free standing as we moved it around. Eventually, all 4 chairs came out, and later the table came came completely too. We did not like that table at all.
We ended up putting the table from our house kitchen in that spot. It was bigger and served a better purpose. Finally, that table was removed also and now we just have a small 4 foot, light weight folding office table there. When we travel, we simply fold up the legs and lay it flat on the floor. No chairs any more.
But to answer your question, 4 screws in the feet of the table, re-attach with the same screws, no problem repositioning the table.
And just for an FYI, those screws will be Robertson Headed screws. They have the square hole and take a square headed screw driver:
Info, click here.