The word нетчик, when it was a thing, was applied only to the nobility.
To answer your question, some modern authors do apply it to lower classes who failed to report for service:
Нетчики сбивались в шайки воров и разбойников, которые порой становились довольно опасными. Подобные банды существовали в Клинском, Волоцком, Можайском, Белозерском, Пошехонском и Старорусском уездах, причем порой нетчики нападали на воинские отряды, конвоировавшие призывников к местам прохождения службы, и отбивали рекрутов. Отбитые, таким образом, сами становились нетчиками и вливались в бандформирования.
I'm not sure it's a good usage of this word, but apparently this journalist's idea of creativity isn't far from yours.
That said, I don't really think the concept of "evading conscription" is applicable to poll taxpayer classes (податные сословия), i.e. serfs and proletarians.
Natural tax duties like military service were not personal obligations for these classes. When a draft was called, it was up to the community (мир) to decide what family would supply the recruit, and it was up to the family to decide on the actual man who was to perform the service. This decision had to be communicated to the draft commission. Some communities implemented turn systems or draft lotteries, others decided it at community meetings.
The family in question had two legal options to avoid the draft: either hire someone who would volunteer instead of them, or reimburse the government for the volunteers hired directly by the government by buying a special document (рекрутская зачётная квитанция). If they were influential within their community, they would rather expend the political capital and pressure the community meeting (сход) to select another family, even if it was their turn to supply the recruit. Of course, all these options and combinations thereof were widely employed.
Before this decision was communicated, there was no personal obligation for anyone to serve in the army.
After it was communicated, the man was technically enlisted. Failure to report for service would count as desertion, and the deserter's family would have to pay or supply another recruit.
So it's not quite clear to me what exactly counts as "conscription evasion" as opposed to "being lucky enough to avoid the draft" or "desertion".