good question - and this is a hard thing to measure experimentally, so must of it is extrapolation from observed data, but the data is starting to be assembled. What we already know is that vaccinated people are less likely to be symptomatic and much less likely to be hospitalised and well, dead. Some vaccinated people can carry a full viral load similar to a non-vaccinated person, but the viral load diminishes much faster, so they are infectious for a much shorter time period (so the Rf number would be lower).
On the other hand, if a vaccinated person does experience a full "breakthrough" infection (full symptoms) then they may be just as infectious as a non-vaccinated person - but we know that vaccinated people are much less likely to have a full breakthrough infection than non-vaxxed people.
TLDR yes vaccinated people can still transmit but early evidence shows the rate is lower. We need to keep monitoring places like Israel though that are ahead of the curve in terms of vaccinations to see if this holds true.
While new data show that vaccinated people can carry high viral loads of SARS-CoV-2, vaccines still prevent the worst outcomes from COVID-19.
publichealth.jhu.edu