I don't think it is perfectly reasonable. During the entire Vietnam war, only 20-30 thousand US draft dodgers fled to Canada, out of a population of 216 million (in 1975). The Vietnam war was extremely unpopular in the US, whereas most Russians support the war in Ukraine. It simply isn't credible that 370K (let alone 700K) have fled to escape the draft.

I think that estimates of how many draft dodgers have fled Russia are utterly exaggerated, probably by a factor of a thousand. I'd believe a couple of hundred. The rest is just "count every single person who leaves for any reason as a draft dodger, don't count people who return to Russia" -- or even just "make up a number out of thin air and attribute it to anonymous sources".

Russia's population is 150 million, of which 370k is about .25%.

Russia's population is less than half that of the USA, but most of them are not eligible for the draft. According to Wikipedia, there are 33 million men and 35 million women in Russia fit for military service. If there really were 370K draft dodgers, that would be over 0.5% of the eligible population. Over 1% if you only count males. It simply isn't credible that 1% of military age males have fled the country in a few weeks. This is "Russia will be out of fuel in two weeks" level bullshit.