Sadly, no. Globe doesn't do that. Anyway, you can call 211 to have your sim reported as stolen. Visit any globe store for sim replacement.
Globe may replace your device ONLY if you have an active enrollment of Gadget Care. But if you do not have an active Gadget Care with your plan then sadly to say you will not get any replacement. Another thing, kindly inform Globe of your concern so they can already flag any calls or text coming from your lost phone so you won't incur charges.