Yes, but only for a while.
It seems as if buying an existing, second-hand vehicle would incur a much lower carbon footprint than a brand new electric vehicle. But, the key difference between an EV and a petrol vehicle is that an EV incurs the majority of its carbon footprint during manufacture. An existing petrol vehicle will be still be pumping out emissions from its engine for years to come, so it won't actually be the more environmentally friendly option for that long.
Example: New 2019 Nissan Leaf
In Carbon Brief's example, a new 2019 Nissan Leaf is compared to an average existing conventional car. They very generously use the average CO² output from a conventional new vehicle (extremely likely to be higher than that). Their chart shows that after 4 years, the EV has caught up with the conventional vehicle and starts cutting emissions from that point on.
There is more on this topic covered on our question Do electric vehicles produce more CO2 than petrol or diesel vehicles?
Article last updated on June 17th 2020.