Yes - Matt Kaeberlein and Allesandro Bitto did something similar about 7 years ago in mice and had positive results. The issue that “brief” or “transient” in mice or drosophila still could translate to a number of years in human terms. And the dose used (at least by Bitto/Kaeberlein) was extremely high (as high as 8mg/kg) - so risk of side effects is also extremely high. And remember - in these lab environments the mice and flies are in pathogen free environments, so risk of immune supression is much less of an issue than for humans who are not in that type of environment:
In male mice, it still extended lifespan almost as good as continuous Rapamycin - but in female mice, it didn’t extend lifespan - there was a trend for 4% lifespan extension - but it wasn’t statistically significant