Can the website start collecting SE users' and viewers' IP addresses this way?
Yes. Hotlinking embedded images is a feature on SE which has been criticized by users in the past. In your example, every visitor of the question page also involuntarily issues a request to the remote SVG image in the background. This way, everyone viewing the question reveals their IP address, user agent string, referrer and other browser details to the - potentially untrusted - third-party host.
Are there other potential problems?
Usually, SVG documents are capable of delivering active script content. So, allowing users of your website unrestricted upload of SVG images would potentially create a persistent XSS threat. However, when an SVG file is embedded as
<img src=...>, as done on SE, the browser blocks it from executing any client-side code. Therefore, SVGs effectively don't pose a bigger threat here than hotlinking GIF or JPEG images.
Another negative effect of hotlinking is that the third-party host could decide to silently replace the image with advertisement or other inappropriate content at any time. (You can find some real-life examples here.)
Specially-crafted SVG files can be used to exhaust your memory. This is known as the billion laughs attack. As a mild DoS attack, it's more of an annoyance than a serious threat, though.
In some browsers it's still possible to conduct advanced phishing attacks by presenting a HTTP Basic Auth dialog for hotlinked images.
I'm strongly in favor of SE enforcing that all embedded images are hosted on a trusted, reliable CDN (e.g. Imgur, as already done with direct uploads). The community rightfully requires text sources to be quoted in case a link becomes unavailable. So it would be only logical to also preserve images in case the image host goes offline. (However, there might be legal implications of automatically re-uploading copyrighted images in a CDN.)