Companies and publishers do not review event submissions other than their own. There is no approval process or consistent veto power, though there are certainly extenuating circumstances.
Usually, the most control companies will influence over events would be something like only allowing specific partners to run officially sanctioned events, or similar.
If you just want to run a variant event, you should be able to do it without any issue. Just submit a detailed submission so potential players know what to expect and do your best to pick a time you think might not overlap with key competing events (though that is more for your own benefit, so players aren't pulled away by the official event).
Gen Con LLC