I presume that if you get all spoke tensions equal, and at the recommended tension for the spoke thickness, then the wheel will be true. My intention is to get a wheel reasonably true (laterally) by seeing where it rubs against the break blocks in situ, and then use the tension meter to fine tune it. Just means I don't have to purchase an expensive stand to measure that the hub is centred, or the rim is over the centre of the axyl. Are these last two measurements unecessary if the tensions are equal?
A wheel could theoretically be trued by tension alone if you started with a perfectly manufactured rim, hub, spokes and nipples and you were building a perfectly symmetric wheel. The reality is that there are minute differences and that tolerances are not all that tight. Not to mention that ultimately the wheel has to go into a frame that also may not be perfect (dishing).
The short answer is no. I've had many sets of hand built wheels that were beautifully crafted and never saw a tension meter because the tension was hand checked. But, they were built in a truing stand and were incredibly close to perfect. Your initial presumption is incorrect.
In short no. I actually took a true wheel that I had built and carefully equalized all the spokes on each side with a spoke meter. This actually put the wheel slightly out of true.
Rims, spoke nipple rim interactions, hubs, etc., are all imperfect. How you place the tension meter on the spoke will be imperfect. All of these little errors can add up to put the wheel out if true.
Use the tension meter to check that you are at a good starting point, then finish the true by hand with a truing stand.
A functional truing stand is a lot cheaper than a tension meter. But you don't need either to build a wheel.
A bicycle makes a reasonably good truing stand all by itself. You can use zip ties to get good markers for getting the wheel properly centered and round.
The problem with using the bike as a truing stand are largely ergonomic. Building a wheel takes time ( especially the first few ) and having it in an easy to use spot, where you can work on it in a comfortable position makes it much simpler.
Hanging the bike or supporting it in some way so you can stand up straight and work on truing the wheel will help a lot.