In 1152, Stephen's position in England was stronger than Matilda's. In 1153, however, Henry II had landed in England with a good-sized army of knights, had some success in the field and some of the English nobles had defected to his side. He had momentum, but hadn't landed a knockout blow and success wasn't guaranteed. Eustace wasn't irrational in wanting to fight on, and he had the resources to recruit an army of his own.
We know that Henry II was an able commander. Whether Eustace was too we'll never know. The outcome of a continued civil war is therefore unpredictable.
Incidentally, increasing his resources is where Eustace's bad reputation came from: he had been extorting contributions from anyone he could, especially church lands, and the contemporary accounts of him come from clerical sources who were, naturally, hostile.
Overall, I think that the best solution all around would be for Henry to become king, let Eustace have a reasonably lucrative lordship as a financial base, and for Eustace to head off to the crusades with an army partly paid for by Henry. Eustace might have liked the idea -- he seems to have been a glory hunter rather than an administrative type, and, of course, he owed the church a penance for plundering its lands.
There is one caveat: Eustace would have to renounce any claim to the crown of Jerusalem if he wanted to be welcome there (the earliest Christian rulers of Jerusalem had, like Eustace, been from the ruling family of Boulogne). So long as that wasn't an issue, the crusading states could use the reinforcements he brought and there would be plenty of opportunities for a man of Eustace's energy.