There’s definitely a difference between a road bike and tri bike. Will the differences benefit your riding style and ability? Some people can read and relate to the differences between the two geometries and understand how the differences might affect their own riding / training immediately. It might not be so clear for others. It is always a good idea to meet with a certified tri bike fitter and have them evaluate you in person.

For most of us, if you’ve been bitten by the tri bug and you plan on training and doing triathlons and multisport events, get a tri bike. For your question specifically, I would say consider the above points, evaluate your future goals, and definitely meet with a certified tri bike fitter and get evaluated. Would a steeper seat tube angle be advantageous? In most cases, yes. Remember, you still have to get off the bike and run. Any energy savings that your quads take advantage of during the bike will benefit you in the run. That’s one significant point in favour of the tri bike.

Because of the forward angles, you can also apply more power down the pedals and the TT bike has some obvious aero-dynamic properties compared with the road bike.

If you were just getting into triathlons and already have a road bike, then sure, by all means throw on a clip-on tri bar and go to town. But if you are buying a bike to train for triathlons specifically and that’s what you enjoy, why even consider a road bike? You answered your own question. Train with what you are going to race with. Ideally…cross train. Don’t trade in that old road bike. Save it…as a road bike. No clip-ons.

It’s not worth much for training. It’s worth more to you as a bike to cross train on, ride with friends and as a spare.
Having a road bike will also allow you to have another choice come race day if the course is very hilly &/or undulated. TT bikes don’t handle very well in corners and hills compared with road bikes. If you want to do Elite races, than you have to use a road bike if it is a draft legal format. There will be regulations as well regarding tri bar length, helmets and wheels…Train safe.