Yes, the bond, when properly made, stays execution on the judgment. He does not need a bond to appeal, but if he doesn't file one, he is exposed to execution on the judgment. As others have mentioned, the bond is more for the judgment creditor in this case since Trump's chances of success on appeal are slim. But it seems to me that if he played paperwork games with this bond and the deadline has passed, he is exposed to execution on the judgment at the judgment creditor's discretion. But to the extent NY and Texas are similarly situated in the law, he did not need it to file an appeal. He wanted it, albeit in a smaller amount. Whether he/his lawyers are playing stupid games, the logical outcome, to me, would be that there is no bond at present and he slow rolls correcting this at his financial peril (which I know is a hypothetical to most and my analyzing it like it's normal leaves this open to dismissive retorts on that basis; but speculation is not what I do).