In short, no. Christian stance against suicide largely results from the interpretation of the Ten Commandments, with St. Augustine pointing out, that the Fifth Commandment being formulated as 'you should not kill' also covers suicide, because it does not apply only to other people, as the Eighth Commandment 'you shall not bear false witness against your neighbor'. This was later upheld by St. Thomas who wrote that suicide contradicts the natural self-love, is damaging to a community and is both a rejection of a divine gift of life and interference in the God's right to end one's existence and thus is an act of hubris. It is quite interesting that St. Thomas' stance echoes some of the reservations towards suicide expressed by Aristotle and Plato. Suicide has been official condemned as a serious sin on the First Council of Braga in 561 that mandated all priests to deny people who committed that deed a funeral on the church grounds. In 860, pope Nicholas I officially classified suicide as a mortal sin that would result in eternal damnation.
This notions were also more or less in line with the ancient Greek attitudes towards suicide. For example, Aristotle was critical of suicide, stating in Nicomanichean Ethics (V.26) that 'killing oneself as a way to escape poverty, love or sorrow is a sign of cowardice rather than courage, because fleeing from difficulties characterizes weakness, so the death is being chosen not because it is morally acceptable but because it merely allows to avoid an obstacle'. In Eudemian Ethics (IV.25) he also adds that people who actively seek death are morally depraved by definition, which sentiment is quite similar to the notions expressed by Plato. The latter summarily discusses suicide in two of his works. In Phaedo (61b-62c), he presents Socrates as generally sympathetic towards Pythagorean attitude that universally condemned suicide, because it is an act against Gods who have put the soul in human bodies as a form of punishment. In Laws he states explicitly that suicide is a deplorable act and people who committed it should not be given proper burial but rather be buried in an unmarked grave. He makes a provision, however, that this should not be applied to people who were insane, found themselves in an irrecoverable position (e.g. were terminally ill), had to kill themselves as form of judicial punishment (as was the ultimate fate of Socrates) or were gravely ashamed of grossly immoral actions. He notes, however, that although these were mitigating circumstances, suicide would still be an act unworthy of a moral person, being only a final act resulting from a depraved life.
Romans, although generally not condemning the suicide of the free citizens on the moral grounds, outlawed the suicide in several cases that had direct economic consequences. The first one was the suicide of people sentenced of capital crimes (as the state could not have seized their property without the verdict), although this law was applied quite liberally. The second was the suicide of a soldier, as the Laws of Rufus mention them among the acts illegal for a soldier and consider them act of cowardice equal to desertion. The third was a suicide of a slave, with an additional provision that if a slave took their life within six month from being bought, the buyer could have demanded a refund from the seller.
Furthermore, an assumption that peasants were living in misery is a misconception that lacks any historical backing and stems largely from the presentistic direct projection of modern standards of onto the past. Peasants were generally neither poor or lived in squalor (from our standpoint they wight have been were, but so have large part of the nobility). They formed the large majority of the society and one can say that until the proliferation of urban centres that started in early 13th century, they were a baseline for an 'average medieval person'. Sure, some were poor, but some were well-to-do and the rest fell somewhere in between. Furthermore, in the Early Middle Ages, when the Christianity was being slowly adopted across Europe, the grasp of the rulers over the local population was far from absolute, with the settlements being largely independent and participating in the mutual exchange, e.g. providing goods and service in exchange for protection, what over time evolved into mechanism that is generally described as feudal relationship.
From the ideological point of view, adoption of the negative attitudes towards suicide were not necessarily a good way to dissuade subjects, as the reception of Christianity among the common folk was a relatively slow process and pretty much never displaced various folk beliefs that fared quite well along the Christian ones during the entire medieval period. It should be also noted that such action was hardly necessary, because folk beliefs, remnants of which can be tracked down to the late Middle Ages (i.e. they were attested as early as that period) were generally pretty much consistent with Christian ones, when it comes to taking one's life. If we assume that such belief stem from the pre-Christian times, then suicide was largely shunned even then, as a substantial part of the supernatural beings in European folklore, especially in Central and Eastern part of the continent were believed to be souls of people who committed suicide. Association of the existence of dangerous beings such as rusalkas or upirs with suicide strongly suggests that the latter was shunned by traditional folk morality across Europe. This also makes sense from the economical point of view, as sudden death of a family member, especially young and healthy one, decreased the working potential of the family, putting it at a risk of famine, especially for the older members, who were unable to work as efficiently or even work at all.
So to sum it up, there is not much evidence that the suicide was imposed on the Christian commoners as a way to prevent the suicides, because nothing indicates that it has been in any way prevalent or accepted in the late Antiquity or Middle Ages. It was rather a natural consequence of the moral condemnation of killing that was also present in various religions and moral systems.