Does omitting "can" change anything?

In your particular example there is a difference.

You react best under pressure. This is an asset.

This states that your reaction under pressure is unequivocally considered an asset. While the first version...

This can be an asset.

infers that it is considered an asset in some set of circumstances. That's because the use of "can be" implies there are also circumstances when it "can't be" true.

There is, in fact, a subtle difference, but for typical everyday purposes, this difference is of no importance.

The remark in question concerns a disposition, a tendency, a feature of somebody's personality. The person has that feature continuously; it is built into the person's character. However, most of the time the disposition is dormant; when the person is not under pressure, the disposition does not manifest itself. It is only when the person is under pressure, that the disposition gets to be exercised.

In 'This is an asset', this stands for the disposition. The sentence tells us that it is, on the whole, good to have this disposition. A disposition's being good on the whole, however, does not guarantee that the exercise of that disposition will always produce good consequences.

In 'This can be an asset', this stands for exercising the disposition, rather than the disposition itself. The sentence tells us that exercising this disposition can be a good thing, but there is no guarantee that it will be so in every case.

The semantic difference is thus in what 'this' stands for, but it would be difficult to think of a scenario in which it would make a practical difference which of the two formulations one chooses.