Yes. A character can become Death Cursed and carry the curse with them to other content.
A lot of this answer is going to cover the basics of the death curse, because understanding the whole thing is required to understand how it works in other content. All quotes are from the D&D Adventurers League ToA Player Primer v1.3.
Acquiring the Curse
The curse [...] is applied to any D&D Adventurers League character playing a Tier 1 or 2 Season 7 adventure after August 15th, 2017, and Tier 1 or 2 CCC adventures after August 24th, 2017.
The Death Curse is something a character has, not the content. The content listed above is where the curse is applied to the character, where it can become cursed. Once the character has the curse, they have it until shed (detailed below).
Activating Meat Grinder
This option is available only while under the effects of the Death Curse. Each player decides whether or not they wish to use it, and their decision only applies to their own, individual characters; DMs can’t make this decision for them. Once made, the decision is final; it can’t be changed. Surrogates can’t choose this option.
At the instant the character picks up the Death Curse, they player can choose to toggle Meat Grinder Mode on or leave it off. That choice is permanent, as long as the character is Death Cursed.
Removing The Curse
Once a character has the Death Curse, there are a few ways out. Other than playing through Tomb of Annihilation (the "Defeating Acererak" option), the character can...
Waiting It Out. Alternatively, characters can wait until others have done their dirty work by retiring from adventuring until the release of Season 7’s Tier 3 adventures (January 2018), or by starting any Tier 3 or 4 non-hardcover (non-DDHC) adventure, and resuming adventuring following Acererak’s defeat. A character choosing this option can’t play Tomb of Annihilation, or any Season 7 Tier 1 or 2 adventures—with or without a surrogate; these doors to adventure are forever closed to them.
Nowhere does it say the character can't be used outside of curse-inflicting content. In fact, the only content restrictions are just the opposite. If the character waits it out, the character is barred from Season 7 T1 & T2 content.
That said, there are two ways "Waiting It Out" comes into effect:
- A character becomes cursed (in the T1 or T2 content above), then levels up to T3 without dying, and plays a T3 module. As soon as they play their first module at T3, the character is no longer cursed. The prohibition against Season 7 T1 & T2 content is irrelevant, because the character is T3 and couldn't play that content anyway.
- A character becomes cursed (in the T1 or T2 content above), and the player decides opts to wait it out. The character is prohibited from content as described above.
Playing Other Content
There is no prohibition against playing other content.
In general, DDAL does not enforce timelining (as another answer implies). A character can be used in any content, in any order. The fact that some material was released before other material does not explicitly mean it takes place in the order it was released. While a timeline can be constructed, the DDAL administration has been reasonably careful to avoid explicitly laying one down for exactly this reason.
In fact, in many seasons (especially Season 5), to get the full story with a single character, you have to play the content out-of-order (relative to release) because T2 and T3 content came out before all the T1 content had been released for the season. To use a pop culture reference, for the most part, a DDAL character's personal timeline is a ball of wibbly, wobbly, timey wimey stuff.
The "hard" timelining only exists for the Season 7 T1 and T2 content and only as it relates to "Waiting It Out". The distinction of "circa Soulmonger" and "post Soulmonger" does not have any bearing on any other content, except explicitly listed above.
Anecdotal Supporting References
In face-to-face conversations with admins, we discussed whether visiting Barovia (Season 4 content) would allow a Death Cursed character to avoid the Soul Monger. I was told that the Soul Monger can't reach across planar boundaries. The conversation was quite specific on the fact that the character still has the Death Curse, and still wastes away if brought back from the dead, but the soul is not collected.