I'm considering changing the bog (as it were...) standard radiator in
the bathroom with a heated towel rail. It's small bathroom and a simple
swap-out would mean that anyone using the basin would be in danger of
burning themselves on the towel rail - which is possibly not ideal.

So the provisional plan is to move the rail to a free wall space above
the bath, and to move the bath - which is being replaced anyway - 20cm
away from the wall, with the space filled by a tiled surface/shelf.
This means there's plenty of room for anyone in the bath to avoid hot
pipes, which will probably be chased into the wall anyway.

This seems fine in theory, but in practice it means the top of the rail
will be some 50cm above the heating pump. And there will be an extra 4m
or so of 15mm piping run both to and from the new rad.

What are the chances of this new load completely unbalancing the rest
of the system - which at the moment seems to work well?

My main concern is that at best the top of the radiator won't get warm.
And that at worst the pump will pump over, and Very Bad Things will
happen.