Setting the Visible property to off will not work, because then the uicontrol does not respond to clicking.
Here are two alternatives that actually work, but are perhaps not as beautiful as an invisible, clickable button.
Button on top of an image
X = imread('drum.jpg');
fgh = figure('Color','white');
image(X)
axis off
axis image
uih = uicontrol(fgh,'Style','pushbutton', 'BackGroundColor','white',...
'Units','normalized','Position',[0.5,0.4,0.2,0.2], 'String','press',...
'Callback',@(h,e)disp('bang!'));
Button displaying an image
X = imread('drum.jpg');
fgh = figure('Color','white');
uih = uicontrol(fgh,'Style','pushbutton', 'BackGroundColor','white',...
'Units','pixels', 'Position',[20,20,200,200], 'String','press',...
'CData',X, 'Callback',@(h,e)disp('bang!'));
Both methods use this image: