There is no a "yes/no answer" to that question. Generally Kalman Filter tends to be better than linear regression, but everything depends on
- the data which you have,
- how you calibrate your model.
I expect that you have used some library for estimating linear regression parameters. Now you need to think how will you "tune" Kalman filter - the constants F, H, R, Q. See Wiki Page of Kalman Filter. I have asked a related question and Kalman Filter parameters tuning is not as easy as in the linear regression example.
General rule is - simple models tends to be better than complicated ones. Take a look at the quote from Makridakis Competitions.
"The most interesting test of how academic methods fare in the real
world was provided by Spyros Makridakis, who spent part of his career
managing competitions between forecasters who practice a "scientific
method" called econometrics -- an approach that combines economic
theory with statistical measurements. Simply put, he made people
forecast in real life and then he judged their accuracy. This led to a
series of "M-Competitions" he ran, with assistance from Michele Hibon,
of which M3 was the third and most recent one, completed in 1999.
Makridakis and Hibon reached the sad conclusion that "statistically
sophisticated and complex methods do not necessarily provide more
accurate forecasts than simpler ones.""