Will it? Can you say that absolutely? The reality is probably that there will be an initial reduction in average speeds but these will soon creep back up as people get used to the layout.
Will it? Even if it does reduce speeds, the other issues highlighted with this particular project may mean that overall the risk to cyclists is increased.
Just to be clear, we need to distinguish between the general point that tighter geometry will reduce speeds and the specific question about how effective this design of roundabout is at tightening geometry. Taking the first point: simplistically, but fairly obviously, people drive faster on straight, wide roads than they do on narrow windy ones; and they go round wide corners faster than round sharp ones. That's way junctions on fast roads have larger turning radiius than those on lower speed roads. The basic principle of what is often referred to as 'continental' design roundabouts is to have much shorter turning radii than is usually the case in the UK, which both reduces speeds and places the turning vehicle more perpendicularly to the flow of cyclists going round the roundabout, thereby improving visibility, see for example this (now fairly old) Traffic Advisory Leaflet:
http://webarchive.nationalarchives....gov.uk/adobepdf/165240/244921/244924/TAL_9-97
Now, one of the ways in which the continental geometry roundabout achieves tighter geometry is to have only a single circulating lane, usually with a wide island that has an over-run area to allow long vehicles to get round, though at reduced speed. This further benefits cyclists by making it harder for drivers to over or undertake cyclists on the roundabout. However, clearly this reduces capacity, so the 'turbo' design uses two lanes, but with lane separators, to try to achieve the same thing. I fully accept the concern that this may not be sufficiently effective, not least because the lane dividers might not be sufficient deterrent. But, as I understand it, the rest of the design does create the tighter geometry, so lower speeds, and better positioning would still be reasonably expected.
Ben makes the point that in the Netherlands these roundabouts are used with segregated cycle provision, rather than expecting cyclists to go round with the traffic. Afraid I can't comment on that, but I do accept that this is likely. However, the broader 'continental' approach is used both with (e.g. the TfL trial design) and without segregated cycle tracks, so I wouldn't rule out using the turbo roundabout for use with mainly on-road cycling, if it does prove to be effective at reducing traffic speeds, discouraging cutting-up and improving positioning for sightlines. So, on the whole, while I understand the concerns, I'd prefer to see how it works in practice rather than dismiss it in advance. I'd add that the cycling officer behind this is most certainly not from the conventional pro-car highway engineering school of thought and probably knows more about international practice and research literature in cycling than most people working in the field.