Yes. You can download the trial version and enter your serial number.
A DVD drive is an optional requirement if you really want to install from DVD. I have not done that with any software for over 20 years. New desktops or laptops do not come with DVD drives these days. Certainly not Macs.
Something to bear in mind is that, I believe, Elements is unique in that the download version is single platform: Windows only or Mac only. But not both.
For the same price, DVD versions sold as a disc in a box come with both Windows and Mac versions.
No idea why Adobe do it that way and only for Elements.