Yeap now with Microsoft support will certainly make mono developers life easier. Still .NET CORE does not contain the amount of features that mono has so it will probably more like replacement of part of the mono framework since core is just a cut down version of .NET.
The fact that .NET CORE is completely open source make things even more clear. A big objection that did not allow mono to be as popular as let’s say Python was that part of mono was replicating Microsoft patented software which made mono a target for litigation and everyone using it. Of course practically most of us knew there was a fat Microsoft would risk the negative publicity but still the landscape is much more clear now.