Very, very broadly, yes. But it is not that simple.
Organisms will, indeed, tend to accumulate more complex genome as evolutionary time goes by.
But there is a big caveat to that is that bigger bloated genomes leads to bigger cells, leads to longer replication times...
So, there are some level of evolutionary pressure to keep the genome size down. This pressure is not uniform, though. It is not a big deal for us, for example. But it has been shown that flying vertebrates, birds in particular but it is also true in the bats to some extend, tend to have smaller genomes.
Similarly, species who live in very highly competitive environment will have a pressure for smaller, faster replicating genomes. Bacteria being a prime example of this, most of their genome to play a direct role.