Essentially yes. The Romans did develop a particularly sophisticated messaging system, based on a series of watch towers, flags and bonfire beacons. In Britain, this sysyem was extensive between forts and along the roads and the coast, and the remains of some of these towers can still be seen in Cornwall. During the Anglo-Saxon period, many Roman sites were often incorporated into an extensive, but admittedly less sophisticated beacon system similar to that which you can see in Lord of the Rings which stretched inland from the coast and also along the Danelaw border.
The Roman system worked on a system of multiple flags, but also had 'crash' bonfires for sending out a generic alert in a hurry when there wasn't time to send a full message. You can see representations of these signalling stations on Trajan's Column, with soldiers atop towers waving banners. The system was supposedly quite sophisticated, with different combinations to indicate the numbers and composition of a hostile force, as well as the vague direction of travel, i.e. "500 horse and 1500 foot moving south".
As to the speed over distance of this system, I can't say, but the Saga of Haakon the Good says that the English-style beacon system installed in Norway by Haakon following his return from the court of Æthelstan could raise the entire country to muster within a week. Sophisticated signals are less instantaneous than a bonfire, but to simply pass a message rather than to also muster a fighting force would streamline things. Perhaps if every single signal station was set up, perfectly prepared and ready to go at all times, it might be possible.
Some reading:
Luttwak (1976), The Grand Strategy of the Roman Empire: From the First Century A.D. to the Third
Reynolds (2013), Landscapes of Defence
Bachrach (2016), Warfare in Medieval Europe 400-1453
I don't wish to be disruptive here, please excuse me; I'm sure no limes were attacked in the making of this post, but for the life of me I don't know what that word in the title was actually intended to be. Lines, perhaps? Can someone please explain?