Yes, of course, but as Hamilton and Jay said above, habeas corpus may not be suspended except by Congress. Many other founders, ratifiers, the Supreme Court, a previous president, etc., held the same view, as you no doubt know.
Congress does not have the authority after the fact to approve an unconstitutional action of a president. They indemnified Lincoln for his actions, but what he did was unconstitutional. A couple of years after Chief Justice Taney's valid legal order (Ex Parte Merryman) against Lincoln's suspension of habeas corpus (which Lincoln ignored), Congress authorized Lincoln to suspend habeas corpus in the last years of the war. If Lincoln had the constitutional power to suspend habeas corpus, why did Congress indemnify his 1861 actions and later authorize him to suspend habeas corpus for those last years.
As the Supreme Court later said in Ex Parte Milligan in a unanimous decision delivered by Lincoln's good friend (and executor of his estate, I believe), Justice Davis:
The Constitution of the United States is a law for rulers and people, equally in war and in peace, and covers with the shield of its protection all classes of men, at all times and under all circumstances. No doctrine involving more pernicious consequences was ever invented by the wit of man than that any of its provisions can be suspended during any of the great exigencies of government." (Justice Davis, ex parte Milligan, 71 U.S. 2, (1866))
From Taney's Ex Parte Merryman order:
The constitution provides, as I have before said, that 'no person shall be deprived of life, liberty or property, without due process of law.' It declares that 'the right of the people to be secure in their persons, houses, papers and effects, against unreasonable searches and seizures, shall not be violated; and no warrant shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.' It provides that the party accused shall be entitled to a speedy trial in a court of justice.
These great and fundamental laws, which congress itself could not suspend, have been disregarded and suspended, like the writ of habeas corpus, by a military order, supported by force of arms. Such is the case now before me, and I can only say that if the authority which the constitution has confided to the judiciary department and judicial officers, may thus, upon any pretext or under any circumstances, be usurped by the military power, at its discretion, the people of the United States are no longer living under a government of laws, but every citizen holds life, liberty and property at the will and pleasure of the army officer in whose military district he may happen to be found.
But never the Supreme Court. As Chief Justice Rehnquist noted in 1996: "The provision of the Constitution dealing with habeas corpus is found in Article I, dealing with the legislative power vested in Congress, and provides that the writ of habeas corpus shall not be suspended unless in time of war or rebellion the public safety shall require it. The question of whether only Congress may suspend it has never been authoritatively answered to this day, but the Lincoln Administration proceeded to arrest and detain persons suspected of disloyal activities."
Silly me. I looked in the Constitution for suspension of Habeas Corpus and discovered that it was indeed in there. After you pointed out that the power to do so was that of Congress, I went back and looked. Yup. It is listed under the powers of Congress, not the executive.
So Lincoln suspending Habeas corpus *WAS* an illegal act, because it wasn't one of his enumerated powers.
I suppose the Union apologists will say he didn't have time to consult congress. He needed to take immediate action because of the rapidity of events. Perhaps not initially, but surely within a week he could have sought for and got a vote on the issue. I would think suspension of rights could have been moved to the top of Congress's agenda.