Tank blitz to Karelia return to Eastern Europe: +2 IPC from income from Karelia. Net +2 IPC.
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Tank blitz to Karelia then Archangel: +2 IPC from income from Karelia. +2 IPC from income from Archangel. -5 IPC from loss of German tank. +2 IPC from optimistic odds on killing a Russian infantry when Russia attacks. Net +1 IPC.
Germany suffers positional loss from loss of forward mobilized tank. Increased income is not placeable on the board until the end of G2, and will therefore not reach the front until combat on G4.
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If it were possible to pull Russian forces out of position with the Archangel blitz, then it would be worthy of consideration. However, it will NOT be possible unless the Russian player is a very bad player. As a matter of fact, blitzing a German tank to Archangel actually HELPS the Russian player by solving the logistics problem of moving infantry from Russia to the front, by putting a German tank on the doorstep of Russia. Since only a few units are needed to recapture Archangel, those few units can be used to trade Karelia with Germany next turn, while the mass of Russian infantry at West Russia trade Belorussia and Ukraine as usual.
The end is that Germany gains nothing in position, loses position, and gains less relative IPCs even with an optimistic estimate of the next turn.
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There ARE some cases in which the Germans should blitz to Archangel. That’s when the Russian player either suffered absolutely abysmal casualties on first round attacks, or if the Russian player was an idiot and moved everything, well, I don’t know, somewhere really amazingly stupid. Since this usually does not happen, I feel pretty safe saying that the Germans should NOT blitz to Archangel.