As written, the Assert rules (p66) don't explicitly say, so it's up to you. But, there are clues suggesting that it's reasonable. Complications are basically the Fixer's Assets, and the game blesses the players using them. ("Complications and Player Cleverness", p 112-113) The game also lets players create assets that change NPCs. "The Role of Assets" (p114-115) in the paragraph about inspired assets. A player might create asset like "Hard Up For Cash" or "Devout Catholic" to change an NPC. And the biggest clue, "An Asset might change the problem—a thug with a gun is best dealt with by your Hitter dice, but if the thug with the gun is Having Second Thoughts d6, that may mean the Grifter can talk him down instead." That strongly suggests that your Hitter might tag the thug with "Having Second Thoughts d6," which the Grifter can immediately make use of.
My suggestion is to allow it. An individual d6 isn't that big of a deal, and it can work in universe. I can see the "Having Second Thoughts" thing happening on the show: Eliot calls outs, "I can see you're shaking, are you having second thoughts?" then Sophie stepping in to close the deal. I can see Eliot being in a tough fight surrounded by thugs, and Hardison, from hiding, sliding out a baseball bat for Eliot. Or from the episode "The Gone-Fishin' Job" (S03E07), Hardison pays for "Distracted militia men d6" which Eliot immediately makes use of make their escape from the camp.