Yes, you could do exactly that, as long as your user_icons directory contains an index.theme which notes the sizes to be used. If your user_icons directory is formatted correctly, what you just described will work like a charm.
The use of Svg's did not cause the error. However, (And I experienced this recently and scared myself and another member of the forum pretty good), if the index.theme does not properly dictate the size of a scalable icon, then it may well scale to its maximum size, causing display issues - freezing, login problems, etc. This is true for .svg, png or any other format. This happens when it tries to build and load an action toolbar fitted with a bunch of 256px icons... Which looks pretty hilarious if you can catch it without freezing your desktop (I have done this a few times)...
The advantage of .svg is that you can have a sized 16 icon that scales up to 256 or 512 without any distortion. Files .svg are Text-Based Images, not raster images.
A sized 16 .png image will look awful scaled up to 256px or 512px...
The downside of .svg files is- if you are working with a lot of them; it can get Tedious doing
One
Icon
at
a
Time
in Inkscape.
If you know a way of Batch Processing .svg image files - By all means please share it.
As it is for myself, whenever I make an icon set, I use .svg files as sparingly as possible, now. I only use them for Symbolic Icons which will be primarily sized 16 but can be scaled to 256 or larger. Part of my bias is that in my sets, sometimes I am dealing with 600 different icons or so or more.
If you have only 20 icons and a little bit of patience, feel free to use .svg files all you want. It will save space and give better small-to-large-scaling.
For large-to-small scaling, .png and .svg look exactly the same scaled.