Most likely not. The price to pay people to get them to do something must exceed the opportunity cost of them not doing that something. Raising an army from your people, if they don't fight alongside you they are probably facing a pretty suboptimal situation - their crops burned, their cities looted, their wives and daughters raped, foreign oppression, etc. This risk may be small, while stepping onto the battlefield has risks of its own, and it requires materiel which isn't cheap, so most people will not do it for free, and even if some will you probably want more and better soldiers as well. But you don't need that much to tip the scales.

On the other hand the adversary stands to gain a lot from pillaging your countryside, both gaining wealth from the loot they capture and security by knocking you out as a potential threat. In the most extreme case they may be looking at exterminating you entirely and taking your land and everything in it for themselves. They may be facing starvation and death if they don't take your resources from you. You fundamentally can't offer them more than they could potentially take. It is rational for them to accept less treasure for sufficiently reduced risk, but there is no guarantee you can offer enough that fighting for the rest isn't worth it in their eyes. Paying them to attack someone else is even harder - they still do not reap the full benefits of defeating you, but they still suffer the risk of fighting, and they have an additional enemy to boot. If they do manage to go for that option, you're almost certainly losing a potential ally (the enemy of your enemy is your friend) and whoever wins that conflict is going to be pretty pissed at you.

On top of this, paying your own people to fight for you strengthens your side. Yes war may not be the optimal use of resources but those dollars are flowing right back into your economy feeding your people, employing your smiths, etc. The strong army you raise both deters potential adversaries and can be used to extract demands from neighbors. Conversely, paying tribute to the adversary makes them stronger - they can afford more men, better weapons, deeper war chests. You may buy yourself time but the fundamental grievances that made war possible in the first place have gone unaddressed; it is reasonable to expect you will wind up in the same situation again at some point, but the next time it will be more expensive to bribe them while you will have less money to raise an army for yourself. You can't repeat this cycle too many times.

All this assumes your adversary is rational. Unfortunately that's not a safe assumption. For the right price you'll be able to raise an army, but whether it be a holy crusade or a fight for freedom or a face launching a thousand ships, a particular army might be fighting for something they consider priceless.

> If you can afford to pay an army you can afford to pay the opposing side instead.

Aside from all questions about how such an agreement is to be enforced once you no longer have the money but the invaders still have their weapons, the article shows very clearly that this is not true. Early states are seriously cash-strapped, and rarely pay their armies in easily portable goods. They can "afford" to raise armies consisting of soldiers who bring their own weapons and, by-and-large, their own food. That does not make for good tribute and so, in fact, they cannot afford to pay off an invader.

There are those who make strong arguments for the opposite.

Once you have paid him the Danegeld, you never get rid of the Dane.