Noteworthy: This path starts with two stop cards. If you can get past those, the rest can be spectacular. That's a big "if."
If you can do something useful with the Peasant's +buy early, great. If the Soldier's terminal silver will help you get a 5-cost you really need, terrific. If it would be useful later to have the Peasant's +buy due to a lack of other +buy in the Kingdom, maybe you buy two or more so that if they collide it's not a tragedy since you were going to keep one anyway. The trick is that this traveller does almost nothing on his own; it's all about making other cards better. So you have to ask yourself: What other cards are you planning on using, and does Teaching them help enough to matter?
Sifting and cycling is just as important as with Page, but the only one that helps with that is Fugitive. Again, getting there quickly enough is the challenge.
A consideration: Teacher can't put multiple tokens on the same action card, and anyone who has played Lost Arts, Training and Pathfinding knows that Lost Arts on a big terminal draw is incredible, as is Pathfinding on a cantrip. But are you really going to buy a bunch of terminal draw cards to collide with Peasant and Soldier? Probably not. So most of the time, you'll be using Teacher for distributing the +1 Card token and then later the +1 Coin token. On a different action. Because there's nothing better to do with it at that point.
The big picture strategy, I think, has to be:
1. Use Peasant to buy multiple cheap engine pieces, maybe even multiple Peasants if you can handle colliding terminals.
2. Use Soldier to buy more expensive engine pieces.
3. Use Fugitive to cycle into buying more engine pieces and exchanging travelers.
4. Use Disciple to double your key engine piece and gain more copies of it.
5. Use Teacher to make the engine pieces better.
I'm sensing a pattern here. The question is, does a Traveller or two speed up the engine building process more than buying other pieces. Maybe, maybe not. It could be a classic "win more" card. Your engine is working beautifully; using Teacher on a key card turbocharges it to the point where it's way overdrawing, a waste of resources.
I played this 4p Colony IRL recently, and my winning deck could only be described as bizarre. I had one Village-variant, a couple of Bakers, and Travellers. I bought as many Labs as possible. Other than the Travellers, I bought no other terminals or money; nothing that would slow the cycling. By the time I was finished, I had put +1 Card on Lab, I had a couple of Disciples who were reliably hitting Disciple-Lab (draw six cards, accumulate an extra +1 Action, gain a Lab. Nuts.) +1 Coin on Baker, which turned out to be more important than I thought it was going to be since I hadn't bought money, and I actually kept a Peasant and a Soldier deliberately un-exchanged since I was reliably drawing my entire deck with extra actions and needed the +buy, and the extra coin and mild discard attack was a nice bonus.
Was it fast to build all that? Not particularly. It worked great once it was done, but I was left feeling like there was probably a faster strategy available, and my guess is that, with this Traveller, you're going to feel that way a lot of the time.
Any synergies? Would a string of cantrip attacks (Spy, Urchin, Minion, Scrying Pool, Familiar,) + Soldier be interesting enough to just get a Soldier or two for a big wad of cash payload? Can you live the dream and use Teacher to put +1 action on Margrave or Rabble for the Soldier payload? is Fugitive/Tunnel a thing? It's easy to imagine all kinds of wild scenarios; making them work, and making them fast is the big issue.