There's also an element of "burning the ships" in that idea; you extend your current operational range at the cost of the logistical capacity (in terms of carried food) of the future. In other words, if you eat all your horses and you're still behind enemy lines, your army is now in serious trouble of not being able plunder enough food to make it anywhere before starving and deserting.
To add to that, we can, with our current technology, for a handful of billion dollars send a rocket to Andromeda that would arrive in 10,000 to 65,000 years.
But if we want the rocket to be anything more than a pitted lump of metal when it arrives, say, sending information back, operating scanners, etc, the price jumps exponentially (assuming any useful technology we build could still be usable even after 100 years in deep space).
It ultimately boils down not to the "Can we do it", but "Is it WISE to do it", and that is always either the more difficult or more expensive question to answer.
> send a rocket to Andromeda that would arrive in 10,000 to 65,000 years
Andromeda is 2.5 million light years away. You are probably thinking of sending some vehicle to the closest star, Proxima Centauri, which is just about 4.25 light years away. This is the same as 270000 AU away; Voyager 1 has been launched 45 years ago, and it's at 157 AU from Earth, which means it traveled at an average speed of about 3.5 AU/year. At this speed it would take it 77000 years to get to Proxima Centauri.
Well, Xenophon and 10000 other Greeks found themselves deep into enemy territory, without supplies [1]. Somehow they managed to survive. They took some food by force, but mostly they used diplomacy and negotiation. Diplomacy is fairly effective when you have lots of weapons.
