Regardless there is no harm in asking. Often this kind of money comes from a different budget allocation at the corporate level than your immediate business group. They may have a ceiling on how much the bg might be willing to give, but on a case by case basis can pull up money from other places to hire or retain someone.
Long ago, MSFT gave me an additional tuition bonus on top of stocks, sign on and relocation. I had indeed asked for it during negotiation. Otherwise at MSFT, MSFT does pay execs and others on a case by case basis for an MBA or similar programmers depending on need and fit.