Now, without knowing what Gundarsson wrote... I can't comment on his theory per se. But I can answer the question with my interpretation based on the things that I know.
Ostara, or Eostre derives from a proto-germanic term meaning to shine, and that also relates to the east or the dawn (and this placement of the dawn and the east, correlates to the "Venus" star of the spring). While evidence is inconclusive, there are references to a possible Proto-Germanic goddess known as Austro. But if we look back to the big old Proto-Indo-European family tree we also see correlating Goddesses in other traditions, including the Roman Goddess Aurora and the Greek Goddes Eos, and even the Indian Goddess Ushas. Etymologically speaking, the names of these Goddesses all are 'in the family'.
But when we look to Idunna, her name isn't a derivative of that same root source.
Grimm, thinks Idunna's name may mean "rejuvenator" and relate etymologically to the Germanic "idis" (essentially a divine female being, or a dignified woman). And while at first passing glance someone may think "oh well rejuvenating is kinda like the spring, when the earth rejuvenates" I don't see it that way. If his theory about the name linking to the idis is accurate, then I think it definitely rules any possible connection out. The idisi appear to function somewhat similarly to the matrons and disir. Sources in lore have them acting as war-fetterers in battle, or as a great mother. As such I see the role as being very different than Eostre. Not to mention her traditional symbol of "apples" is all out of season. For apples are ripe and ready to be eaten in the fall.
Furthermore, if we think in very vague general terms about ancient rites and what was going on in the calendar year we see a pattern emerge. Since this was very much an agricultural religion, much of the holy tides revolve around the necessary life cycles. Spring was about re-seeding life, and new life, and new growth. Summer was the continuance of growth 'maintenance' of the crop, and also the time for war, travelers, and traders. The fall marked the harvest of the crop, and preparations to survive winter. And winter was a time to hold up, rest, and sleep, and a time of death as well.
In human terms, spring is one's youth, summer is one's prime, autumn is one's slow graceful decline, and winter is a life fading to age, illness and eventually death. It does not make sense to be given the fruit of immortality when you're a babe, but rather to be gifted with immortality when you are of an "autumnal" age where you can appreciate the gift, and have the wisdom and experience of life behind you.