For SLI (Gaming) the model matters, they need to be the same. For machine learning, no it does not.
As for the box, you really have 3 options, and it depends on what you want to do:
You can go a cheaper option like AMD or a smaller processor (I highly recommend away from AMD, it is cheaper for the chip, but the rest of the components are regular price so the savings on a high end ~$2000+ system is only like $100-$150 and Intel is almost always faster. Going a smaller CPU will slow down your EPOCHs a bit and bottleneck (limit peak performance) the GPU but the CPU isn't a huge factor (think 5-20%), GPU is king. If the server is only going to be used as a headless (no monitor, not interactive) Deep Learning box, then this is fine, but I still recommend against this personally. Just like using AMD, the difference between a mid level and top level CPU isn't big when you start factoring in $400-$1200 GPUs (think $100-200 tops).
The second option is what I have, I use my desktop heavily for all sorts of things from AAA gaming, game development, photography and deep learning. So I went with the best Intel I can get for raw single core performance (Intel 7700K). I only have a 1070 but I am considering two 1080Ti's really soon when the MSI comes out with their gaming X models (faster stock speeds and infinitely better cooling, the cooling is important for gaming but absolutely critical for machine learning and I think this is underestimated as the stock cooling is awful).
The third option is a true server build, this involves using Intel Xeon processors rather than the traditional desktop processors. The benefit of this is you can break out of the traditional 4 core chips and go into 8 and 10 core as well as multiple CPU for a total of 40 cores+ with hyperthreading. You also get 40 PCI Express lanes, which allow you to run your GPUs without any bottlenecks. Even on a desktop 1-2 GPUs with newer boards (PCI Express 3) won't be throttled until you drop down to 4x which is typically when you have 3+ GPUs (single card runs at 16x, two cards at 8x, and 3 cards 8x 8x and 4x). Each NVMe drive also takes away 4x so if you run 3GPUs you will sacrifice the speed of two GPUs to use it (8x 4x 4x and 4x for NVMe).
Basically, the way I see it, I would not opt for option one (cheaper CPU/components and focus on high-end GPUs, I'd just get a high-end GPU, you already at the thousands, another $150 to get the best CPU isn't go into making a big difference in cost). If you are using it for interactive work or your main desktop, even more of a reason to do this. The only time I would recommend AMD or cheaping out on the CPU is if you are going low budget $500-$700 machine, cause it will allow you to get a super cheap box, but once you start getting up over $1000 I would recommend just getting the best CPU available.
If you want a dedicated server, you plan on going up to 4 GPUs and want the best setup you can get, and have a "power-house" deep learning box, I recommend the Xeon route. Xeon's are better overall but are poor choices for Interactive desktops and Game machines as the CPUs are slower for 1 thread processes (which most work is) but have a lot more cores but more important twice the PCI Express buses. If you do not plan on 3 or more GPUs, this isn't the best option. If you plan on 1070's you can probably get 3 of them at full speed without even going Xeon with the 40 lanes because it just isn't fast enough to bottleneck heavily even at 4x. If you are going to share with other people, or plan to do a lot of jobs in parallel, I would lean towards Xeon as well.
tl;dr Unless you building the cheapest system you can possibly build, don't cheap out on the CPU and buy AMD or lower tier. The price difference is tiny and performance significant. If you build a multi-user server or plan on going 3+ GPUs, go Xeon unless it is your interactive desktop then you might want to stick with Intel 7700K or Intel Extreme.