This is an interesting consideration.
Another issue is deep water navigation.
How many "trips" do you think that the Traveller would be able organize and partake in? What's a good time line for a trip like that? Three years? Five years? And how much usable life span would he have? 20 years? 30? Not even counting folks getting ticked off and just outright killing each other (for assorted reasons), but just this kind of activity is flat dangerous.
Using the scout/courier, he could fly to the Amazon rain forest and start looking for rubber trees immediately, but perhaps he ought to work on giving the Roman's an independent ability to travel there. The Roman's already know how to make wooden ships and sails, so they need more advanced sailboat designs and a means of navigating across the ocean as well. I'd say they will probably be ready to do that in about a year from the Time Traveller's arrival, so about the spring of 114 AD would be a good time to set sail.
The Time Traveller is not a skilled craftsman except in his trade of stealing things. Many of the files from the library can be translated into Latin, but perhaps it would be a better idea to teach Roman craftsmen Galanglic so they can read the files themselves and figure it out. In two to three years they could learn to make steel, and following diagrams manufacture firearms in about 3 years I think, or the year 116 AD, cannons are just larger versions of firearms, so the Emperor will have his men producing both cannon and muskets, and or rifles. Magnetic compasses should be in hand, and the Time Traveller can print out a map of the local sky from the Ship's astrogation program, correcting for the current year of course. Mechanical clocks would also be important and astrolobes. By 116 AD it will effectively be the 16th-18th centuries technologically. In 10 years expect the development of the steam engine, with the ability to make magnets for compasses also comes the ability to create electrical generators, and batteries, wires, telegraphs, and primitive radios. In 20 years a number of railroads will be built crisscrossing the Empire, I'm sure the Emperor, whoever he is, will be big on building those railroads.
By about 153 AD the first internal combustion engine will be built, by about 163 AD, Rome will fly its first airplanes, by about 193 AD the first Roman jets will take to the skies, by about 210 the first Roman satellites orbit the Earth, Roman astronauts walk on the Moon in 215 AD and plant the Imperial Eagle in the Moon's soil. By about 225 the first Roman nuclear bomb is detonated with a fusion bomb being tested by 230 AD.
The Roman's are in no big hurry with nuclear weapons as they have already conquered the parts of the globe they want to conquer with conventional weapons. The Roman's build their first nuclear fusion plant by 250 AD, they also have a colony on the Moon and Mars by this time. In 270 the build their first Jump Drive and explore the Alpha Centauri System colonizing Prometheus. (They kept the name from the Ship's charts having no reason to change it) the Roman's need to do 2 successive Jump-1s to make it to Alpha Centauri since they are only tech level 9 at this point. They reach TL10 by 300 AD, TL11 by 320 AD, TL12 by 340 AD, TL13 by 360 AD, TL14 by 380 AD, and finally TL15 by 400 AD at which point they caught up with the Third Imperium. The Roman's then get curious about the Time Drive, the Time Traveller is long dead by this time, the Roman's fiddle with it, and pay a visit to the OTU. Because of some trips the Time Traveller made at slower than light speed to nearby stars, the date when the Roman's visit the OTU is around 1201 Imperial. After some fiddling, they manage to open a stargate back to the OTU and they send some ships through. One thing they notice is there are more habitable planets in the OTU than in their own Universe. After exploring space for some time in their own Universe they noticed no sign of the first Imperium, and no sign of the Ancients, so it appears the Roman universe is more different from the OTU than originally thought. Since the OTU finds more habitable planets in the OTU, they send some ships through to colonize them. It appears that the Third Imperium has collapsed, the Roman's find no problem with this and just move right in to take its place. Lots of abandoned space stations with dead humans in them, the Roman's have no idea what caused this and the Time Traveller is dead at this time. So the Roman's just push through the gate and do what empires always do.