It is possible using undocumented MATLAB functions. The trick is to catch when a datatip is changed and update the others accordingly.
A proof of concept with two linked plots is shown below:
% first plot
f1 = figure;
p1 = plot(1:10);
datacursormode on; % enable datatip mode
c1 = datacursormode(f1); % get the cursor mode
d1 = c1.createDatatip(p1); % create a new datatip
% second plot
f2 = figure;
p2 = plot(1:10);
datacursormode on;
c2 = datacursormode(f2);
d2 = c2.createDatatip(p2);
% register the function to execute when the datatip changes.
set(d1,'UpdateFcn',@(cursorMode,eventData) onDataTipUpdate(cursorMode,eventData, d2))
set(d2,'UpdateFcn',@(cursorMode,eventData) onDataTipUpdate(cursorMode,eventData, d1))
% callback function when the datatip changes
function displayText = onDataTipUpdate(cursorMode,eventData, d)
pos = get(eventData,'Position'); % the new position of the datatip
displayText = {['X: ',num2str(pos(1))], ...
['Y: ',num2str(pos(2))]}; % construct the datatip text
d.Position(1) = pos(1); % update the location of the other datatip.
end