Assuming they have a moment to piece things together, a well travelled Roman would almost certainly be able to recognise geographically distinct locations. Britannia is the large island to the left, Italy is the bit kicking Sicily, Greece is the bit with all the little islands, Egypt has the Nile in it, and so on.

For example, here is Strabo's map of Europe produced in the 1st century BC. He clearly understands the rough shape of places like Italy and Iberia: https://upload.wikimedia.org/wikipedia/commons/8/88/Map_of_Europe_according_to_Strabo.jpg It's a rough map and places like Britain are almost all wrong (though in fairness very few Romans had been there in his time) but it is recognisably Europe.

By the 2nd century AD Ptolemy's atlas displayed the shape of Europe in even more accuracy: https://i.pinimg.com/originals/f7/5e/76/f75e762f4502b020adb777d31a2a0391.jpg

So yes, I think it's fair to say that if you grabbed someone from Rome, pointed to Italy on a modern map and asked them what it was, they'd probably recognise it as Italy. But if you asked them where Lundinium was, they'd probably have no idea. These maps were not used for general navigation, they are just not detailed enough for that. At most they might be useful to long distance sailors, especially Ptolemy's because it lists as many ports as he could fit on the page, but for the most part these were intellectual exercises. If someone wanted to get from Rome to Revenna these would have been almost completely useless. But there were maps for that.

In the 4th century AD you have the Tabula Peutingeriana. The Tabula Peutingeriana is a 13th century manuscript but contains a map of the Roman road network. How much of it is the original map verses a medieval scribe's artistic rendition of an original is up for debate, but it preserves the most important thing - the roads. The geography is rather poor, but that's like complaining that a map of the London Underground doesn't accurately show the Thames; it's not the point of the map. This could be used to get from one town to the next, it even labels the roads so you can follow the signs: https://static1.squarespace.com/static/558dadc5e4b0813627c48032/t/57bdda575016e1f481197164/1472059996654/?format=1500w

It's worth noting that ordinary people such as soldiers could understand and draw basic maps. We know this from a preserved shield from Dura-Europos on which a soldier painted what must have been a brilliant map of his travels: https://static1.squarespace.com/static/558dadc5e4b0813627c48032/t/5a5c0084e2c483cd419b9b25/1515978892820/dura+map.jpg?format=1500w

Then you also have the even more precise military navigational guides, as Vigetius tells us in his De re militari:

Indeed, the more conscientious generals reportedly had itineraries of the provinces… not just annotated but illustrated as well, so that they could choose their route when setting out by the visual aspect as well as by mental calculation

Another thing you might be interested in is urban maps. Rome was a big and busy place and the Praetorian Guard, firefighters, new officials etc. needed to know where to go. We have some pieces from a giant marble map of Rome called the Forma Urbis Romae which plots out the city in exquisite detail. The scale is a bit off and a lot of building interiors are probably interpolated, but still: http://4.bp.blogspot.com/-oXPp4CQh0ZM/ThaVIAb3zdI/AAAAAAAAAU0/7xlGn3MvV6Y/s1600/Forma%2BUrbis%2BRomae.jpg

So actually, they probably would recognise a modern map. The details might need explaining, but it wouldn't be that alien to them.