If it were mine, I'd not be concerned. Of course, all things are possible, but IMO, this is way down on the list of worrisome things.....like falling off the list.

Birch are nice trees, river birch is probably the best one for where you are, and yes, roots can do some mighty feats. But as trees go, no birch really lives all that long-usually 100 yrs. being tops-and within that timeframe, I just don't see anything happening to cause trouble

If you really must worry about this, perhaps a sheet of copper flashing, dug into the interface beween slab/ground would ward off any roots to where you won't most likely even live there anymore. Or, one of the Typar barrier fabrics. Not saying I'd do all that, but one could.

+oM