"Can the estate pay the tax if the income has not been distributed, avoiding K-1 to beneficiaries?"
It cannot do so and also be in strict compliance with the Internal Revenue Code and Treasury Regulations.
Income for the taxable year that is required to be distributed currently to the beneficiary(ies) is included in the gross income of the beneficiary(ies) whether it is actually distributed or not. See IRC §662(a)(1), Treas. Reg. §1.662(a)-2
[note that the IRS is probably not going to put up a huge fuss if an estate or trust insists on paying income tax at the ridiculously compressed tax rates applicable to those entities if income was not distributed but retained. However, handling the affairs of an estate or trust in such a manner is neither in compliance with the tax law nor with a will or trust instrument that requires income to be distributed currently]
