Yes, it is true, you can write the equation for the age of the universe that way. . But it is not a much used equation because the f term is not so simple.
The reason you can write it that way is that both 1/$\sqrt(\Lambda)$ and 1/$H_0$ have the dimensions of time, about $10^{18}$ seconds
You can get the number for the current Hubble constant and get your numerical value of f, but not clear at all that it helps much in thinking through things. f in fact depends on the cosmological constant also.
The best equation for getting the age of the universe is
$t_0$ = F/$H_0$
Where the denominator is the current Hubble constant. F (different from your f) is .956, per the current concordance model of cosmological parameters. However, F is also a not so simple equation. But at least close to 1. The inverse of the Hubble constant is about 14.4 GlyGy, and the age of the universe about 13.8 GlyGy.
See the wiki article at https://en.m.wikipedia.org/wiki/Age_of_the_universe
See the equations and values for the cosmological parameters at https://en.m.wikipedia.org/wiki/Lambda-CDM_model, where they use numbers for the Planck collaboration(latest). It also has the equation for the Hubble parameter