This is probably opinion based but I've played this game many many times and was involved in the play testing of the expansion.
Its my view that TTA is more a tactical game than a strategic game. If you approach it with a long term strategy and that cards you wont don't appear till late in an era, get taken by others or that elusive tactic you want doesn't appear you cant do much about it. I'd advice playing the game more reactively and assessing each current situation rather than trying to plan to much long term.
if you think you will suffer being the weakest player there are many things you can do to mitigate this.
1) Don't play events. the points you lose not doing this is very small compared to what the final score are likely to be. If your not playing events then the events you don't want are less common.
2) Play colonies if you have them. If you can bid enough for a stronger player to have to keep rebuilding their strength then the won't be spending resources of other things.
3) Try to compete with strength. As with all board games its not about having the largest score, its about just have a larger score than your opponents. If you need to spend a bit building an army rather than things that score points then do that. Having an awareness of the tactics and trying to pick up at least one cavalry or infantry units card will help.
I wouldn't say that the military strength aspect is to important. But it is something you have to just be aware of when making decisions as its one of many factors in the game. With the exception of wars I don't think the negative effects are that devastating if you know what might be coming.