Yes, the officer corps of the New Model Army was far less aristocratic-centric than English armies both before and since but the reasons behind this were not so simple.

Fundamentally, the New Model Army was brought into formation (1645) after the Self-Denying Ordinance (1644) had been passed. The Self-Denying Ordinance was passed by Parliament to remove all Members of Parliament (Lords and Commons) from positions in the military. This was primarily because the radical elements in the House of Commons believed it would be better to remove the aristocratic influence from the Parliamentarian forces to limit their influence over the course of the war, and importantly, the ongoing negotiations with the Royalists. All of which predated the New Model Army in both design and perceived need.

The Army itself was formed for various reasons, but by the time the formation (I would argue reformation) there were still some scions of noble houses serving in various armies of Parliament, just none who also held seats in the House of Lords. The process of reforming the regiments into the New Model also meant that many small and understrength units were consolidated or disbanded and their surviving rank-and-file transferred to the remaining regiments. This did leave an excess number of officers compared to those available. Some of these were encouraged to serve as private soldiers, but there does appear to have been an opportunity to remove the last of the influence of the Lords from the reformed army both by selected regimental commanders who were deemed as 'sound' and by influencing the appointments to the lists of regimental officers. As such, many of the officers in the New Model were selected from either 'professional' soldiers - men who had served pre-war in armies in Europe, and/or veterans from the preceding seven years of mobilisation.

I am happy to answer any follow up questions on or around this.

TLDR: Yes, it was. But rather as a result of deliberate political choices and internal-Parliamentary conflicts rather than solely seeking a meritocratic officer cadre.