It depends. If you want something like Opera or Firefox it won't run at all. If you are satisfied with basic functionality then you can use browsers like w3m which work well on low-powered devices. I think some developers will find a good compromise between performance and functionality.
And by the way, the very first R5 already runs with 320 MHz :-)
But there is still a very long way to go. Clock speed is not the only determinant of processor performance. Even low end laptops like the ARM-based Chromebook have out-of-order processors. The Rocket CPU used in the HiFive board is an in-order machine. There is an out-of-order implementation called BOOM, but it is not quite as mature. Whereas Rocket has been taped out and validated many times in our Berkeley test chips and now in SiFive's commercial silicon, BOOM has not yet been taped out.
And I'll be the first to admit that RocketChip is not nearly as reliable as you would like for a consumer product. SiFive's done a lot of work to improve the system, but there are probably still outstanding bugs in the memory system.
They run fine; I find Voyager 3 to be a bit bloated, but IBrowse runs quite well.
As others have mentioned, text-based browsers like w3m will probably be even smoother (although I usually run w3m via emacs-w3m, which would probably be much slower than using a normal terminal interface).
OTOH this rules out laptops that OP wanted. OT3rdH ARM started with devices like these in mind, but went all the way to pretty powerful, desktop-comparable machines like current smartphones.
Open ISA and open hardware should be a major security concern for most countries.
Why should R5 compete with the big players? It doesn't need to support the bloated OSes. It would be sufficient if Linux runs with acceptable performance. If Linux is able to run on a 12 MHz 68k [1], and SiFive already runs with 320 MHz [2] then I think we don't have to wait too much to get a suitable cpu, since it could also be a "weak" massive multicore, or we could stick multiple cpus together in a cluster.
By the way, Fabrice Bellard has already published a Linux/R5 emulator [3]. As for me, I am really excited about the R5 movement!
[1] http://www.bigmessowires.com/68-katy/
[2] https://www.crowdsupply.com/sifive/hifive1
[3] http://bellard.org/riscvemu/