VS Code v. 1.21.0-insiders
OS: win7x64
When your plugin is enabled - somehow it disables the Emmet suggestions in VS Code.
It comes like this in .html file.
take a look at it:

_(clickable)_
Is that the plugin's fault, or the VS Code's one?
I am having this same issue. Once I install the plugin, Emmet no longer works.
Impacted by this issue too. Actually, the Emmet still works, you can just type, for example, "mycustomtag", then type a space after word, then delete the space and the last character (in this example "g") and then after retype "g" you'll be able to hit
Similar to https://github.com/angular/vscode-ng-language-service/issues/177, will track this issue there.
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Most helpful comment
Impacted by this issue too. Actually, the Emmet still works, you can just type, for example, "mycustomtag", then type a space after word, then delete the space and the last character (in this example "g") and then after retype "g" you'll be able to hit to get your abbreviation expanded.