There isn't an "end turn" button for players, no. This could be more effort to implement than it's worth. For instance, how would you determine who gets to end their turn? Control of the token? What if the GM doesn't want players to be able to end their own turns? Would you add a check box as another option to each token? A global option? Much easier to have the players just say "I'm done" and have the GM click the button but maybe I'm underestimating the appeal of players being able to click it instead. To directly your questions...no. It's possible they could implement it in the future but I haven't seen any discussion about adding it. Hope that helps.
The same could be said about giving players the ability to edit their initiative, except ending turns happens a lot more often than adding initiative. If you factor six players and 10-20 seconds of lag time / players assuming the GM knows they are done / spacing out, that adds up over the course of a game. Plus it is kind of a hassle to have players verbally say 'I'm done' each and every time. The other side of the coin, there is little downside to having players click when their turn is over, especially given how my groups tend to have side chats during combat, multitudes of 'I'm done' gets in the way of things.