TL;DR: Yes and no. The most relevant grammar structures are:
- 没 + [verb] (with no 了), e.g. 我今天没吃饭 (I haven't eaten today);
- [duration] + 没 + [verb] + 了, e.g., 我一天没吃饭了 (I didn't eat for one day);
- 没 + [noun] + 了, e.g., 我没有米饭了 (I don't have rice [anymore]);
- 不 + [verb] + 了, e.g., 我今天不吃饭了 (I won't eat today [anymore]).
These last two use the change-of-state 了.
(I'm a learner, so there may be exceptions I'm unaware of. In writing this answer, I tried to cross-check as much as reasonably possible.)
1. Negating past actions
The most relevant grammar structure is the following.
Subj. + 没有 / 没 + Verb
Negation of past actions with "meiyou"
This should be thought of as the default:
I haven't eaten breakfast today
There's no semantic distinction between 没 and 没有 here: pick whichever is most suitable in the given context.
Adding in a change-of-state 了 here, if it isn't plain ungrammatical (i.e. no state is being changed), is probably going to sound weird. This was emphasized in dan's answer. As another data point, this Zhihu article (although not a reliable source for grammar) talks about how they feel 我还没吃饭了 (I still haven't eaten) is a regional dialect, with one author writing ...这个语法很奇怪 (this grammar is very strange). However, this doesn't stop it being used: see Baidu
"我还没吃饭了". As an aside, we can use the modal particle 呢 here: 我还没吃饭呢.
2. Duration of inaction
Using 没...了 with a verb ordinarily (always?) implies we are using the construct:
Subj. + (已经 +) Duration + 没 + Verb + 了
Expressing duration of inaction
(I'll ignore 已经 for simplicity.) In the running example, 今天 is not a duration. So here's another example:
I, [for] more than twenty hours, have not eaten anything
If we wanted to use this grammar structure with 今天, we could say:
Today, I haven't eaten all day
3. Change of state (noun)
If you're anything like me, there might be confusion with
没(有) + [Noun Phrase] + 了
Expressing "not anymore" with "le"
It's the change-of-state 了, for when we no longer have something. For example:
in 2050, [there] will be no chocolate [future change of state]
4. Change of state (verb)
If we want to highlight a change of state for a verb, the appropriate grammar structure is:
Subj. + 不 + Verb + 了
Change of Situation in the Negative
In this case, there's some variety, such as:
I won't eat tomorrow [change of decision]
From today on, I won't eat meat [current change of state]
I, for many years, have not eaten pork [past change of state]
Above we have a change of state, but (for contrast) below we don't (so no 了):
Hui Muslims don't eat pork [no change of state]