I think it would depend on the agent's intent.
The reason why one becomes liable for carrying when the item was predesignated is that the predesignation shows us that the carrier is carrying the item for the specific purpose (in the case of a seed, to plant it), and that shows that he considers the item "significant". Even though someone else carrying the same item would be exempt because it is "insignificant", by predesignating the item the carrier has made it significant vis-a-vis himself.
Predesignation is just one example of creating "significance". In fact the Talmud immediately asks why the Mishnah spoke of a case of predesignatioon, and not simply a case of someone who took out a seed to plant. The Talmud answers the Mishnah is teaching us that even in a case where the person forgot what he had designated it for, so it is unknown why he is currently carrying the item, he is still liable for carrying any size because we follow his original intent when he designated it and we consider it "significant" vis-a-vis him.
This indicates that the designation is not necessary to make one liable. As long as one clearly carries for a purpose which shows "significance" then he is liable. This is clearly stated by Rashi there:
ודאי מוציא לזריעה חייב ואף על גב דלא אצנעיה מעיקרא ומתניתין דבעי מצניע
במוציא סתם קאמר כגון לטלטלו מבית לבית דאינו חייב אלא משום דאחשביה
This is also clear from Rambam's codification of this law. In Hilchot Shabbat 18:20 he first mentions the case of one who carried the seed in order to plant it, and rules that he is liable, and only in the next halacha does he introduce the idea that predesignation is enough to make him liable when it is unknown why he is carrying it:
במה דברים אמורים שאינו חייב אלא על ההוצאה כשיעור כשהוציא סתם אבל
המוציא לזרע או לרפואה או להראות ממנו דוגמא ולכל כיוצא בזה חייב בכל
When does [the abovementioned rule,] that a person is liable only when
he transfers the minimum of a standard measure of a substance, apply?
When the person transfers the substance without any specific intent.
If, however, a person transfers a [seed] to sow, or a substance for
medicinal purposes, to show as an example, or the like, he is liable
for the slightest amount. (Chabad.org)
המצניע דבר לזריעה או לרפואה או לדוגמא ושכח למה הצניעו והוציאו סתם חייב
עליו בכל שהוא שעל דעת מחשבה ראשונה הוציא. ושאר האדם אין חייבין עליו
אלא כשיעורו זרק זה שהוציא כבר לתוך האוצר אע"פ שמקומו ניכר כבר בטלה
מחשבתו הראשונה לפיכך אם חזר והכניסו אינו חייב עד שיכניס כשיעור
Should a person who stores a substance to use as seed, or to use for
medicinal purposes, or a substance to be shown as a sample,
[afterwards,] forget the reason for which he stored the substance,
and remove it without any specific intent, he is liable
regardless of its size. Another person, by contrast, is not liable
[if he transfers this article] unless it is of the prescribed
If after transferring the article [for the intent he originally had],
the person throws it into a storeroom, even if it is [set aside] in a
distinct place, his original intent is considered to have been
nullified. Therefore, if he brings in the article afterwards, he is
not liable unless it is of the prescribed measure. (Chabad.org)
From the above we see that predesignation has no inherent effect on Shabbat-violation-liability; it is simply a metric used to determine why the carrier is carrying it. When the carrier is the one who made the designation then the designation is relevant to determining liability (in the backhanded sense that it shows his intent). When the carrier is someone else, however, the designation is completely irrelevant because one person's designation doesn't speak to another person's intent. There could, of course, be other factors that could demonstrate that an agent does consider an item "significant" despite lacking the normal size requirement, but these factors don't necessarily have anything to do with whether the item was predesignated or not.
Thus, to answer your question, the agent would be exempt because there is no indication that he considers the seed "significant". If, however, there was some other indication that the agent does consider the seed "significant" (and one could perhaps argue that accepting the mission is such an indication) then the agent would be liable, but not because of the predesignation.
The sender/designator would be exempt regardless, because he did not violate any Shabbat labors.