It is exactly the opposite- a good crown on the neck allows you to push less (and less accurately in my findings) because the string contacting the fret surface area is less. I have a few vintage ukes with worn frets and they are a bear on some chords- my Martin Gets a death grip on B flat every time or it will buzz (part of the fun for me with really old ukes), and all my May Bells have a funny fret here and there. SOme day I will fix them and be totally lost because I played them so much while they were jacked. Frets in a set-up uke are filed first to assure they are at the same height, and then re-profiled or crowned to be round.
With an Em chord buzz, it could be a fret issue (easily isolated- play a single not on each string from the nut down until you get a buzz), but more likely than not it is a fingering issue if you are new to the Uke. Em, Bb and E will give you fits for DAYS, but they will all sweeten out with practice.
Most factory ukes are set High- there is a reason for that. If a player "over-strums", or is just that punk rock, they will get a buzz if the action is low. SOme folks like (need) a higher action because their attack does not work at a low one. I bought a Uke from Jnobianchi that he played beautifully, but I new he was far more ginger in the strum department than I am. When I got it, I could not play it without it buzzing, but that was all action, not the Uke itself. I raised the action and it plays like a dream for me...while he would pick it up at this point and think it was rubbish. Does that make sense? Different strokes for different folks. The only uke I have had commissioned to be set up by a luthier required I played it for him before he did the work ($20). He watched me play a few tunes and did his thing and knocked all the buzz out of it for me in about an hour.