Does Natsu Dragneel retain his ability to utilize some of the non-dragonfire elemental magic he eats?

Natsu's consumption allows him a temporary release of other elements from what he has consumed. It is not a permanent thing. When the energy of whatever he has eaten subsides, the power washes away.

There is a possibility he retains the power although it frequently has to be refilled. If you payed attention Natsu says he had created a vessel for the black fire and the lightning so that he can use it, but since Zancrow died he can't refill his black fire, and Natsu would need Laxus to give him more of his lightning for Natsu to use the lightning-fire dragon combination again.

It was Confirmed that he can retain the ability to do so, but the specifics are sketchy. It appears it is temporary unless the magic is dragonslayer magic, as including Natsu, 3 of the 7 dragonslayers have obtained secondary elements which they have used without the sources, and all 3 secondary elements are obtained after eating another dragonslayers magic. Natsu has indeed eaten Etherion lacrima (numerous magic elements in one), as well as Godslayer flames, but he has never used those magics after the fight was over so far in canon. I have no idea how far the English Dubbed anime is, and since this is not on the anime stackexchange, i'll spoiler the other 2 as well as some prime examples just in case (Everything here has been shown in the subbed anime already)

Gajeel obtained Shadow dragonslayer magic from Rogue of Sabertooth, and Future Rogue of Sabertooth also Obtained a second element by killing his comrade Future Sting, the Holy/light Dragonslayer, before he traveled back in time. Future Rogue fights Natsu with both shadow and holy, while natsu fights back with fire and lighting, neither having the source dragonslayers for the 2nd elements nearby. Gajeel Consumed Shadows from Present Rogue in the Grand Magic Games, and later used his shadow/metal powers alongside Natsu also using Fire/Lighting against 2 of the Tartaros Demons. It is also noteworthy that Present rogue did not display that he obtained Holy Dragonslayer magic yet like his future version had since the timeline had changed.

It is unknown if 2nd generation dragonslayers (the ones with dragon lacrima (magic crystal)) can eat other elements (Laxus and the Poison Dragonslayer whos name i cant remember)

As an fun fact/exception/special case, in the most recent chapters of the Manga which is fairly far ahead of the anime right now, there is

a new dragonslayer, the strongest of the 10 wizard saints, God Serena, has (i believe it was) 7 dragon lacrima in his body or so, and therefor has 7 dragonslayer elements he can freely use, as each Lacrima is a different element.

Though, i suppose if you wanted to get technical, Acnologia is a dragonslayer as well, but we have no idea what elements he has.

There hasn't been any specifics of weather or not he can retain all of the magics besides that of other dragonslayers after the time he consumes it and can use it for a brief period (Such as Zancrow)

As to the comment above, Acnologia's element was revealed, well actually in the most recent chapters he says himself that he has no element and can eat any magic in existence.