If your response is to be a paper you can answer either way. Let's say you argue, "No." Here's a good way to structure your paper.
First, establish a definition of "formal declaration of war." In the 1700s nations declared war on one another in essentially the same way as they do today -- it just took a little longer for messengers to arrive at each nation's capital with the declaration. If you have time to research, you may want to cite names of ambassadors of any two nations (e.g. the ambassador from England to France; Germany's ambassador to Spain, etc.), how they communicated, or even how they were recalled in cases when two nations were in a dispute that lead to war. You might want to pick two examples of how war had been declared by, England, France or Spain, prior to July 4, 1776 -- since those nations were at war with one another off-and-on over a period of two centuries.
So, in developing your paper you might follow this structure:
1. What does it mean to issue a "declaration of war?" European nations in the 1700s routinely fought battles between one another without declaring war. So, after the Battles of Lexington and Concord in April 1775, everyone knew there would be a fight between armed forces of Colonies and Great Britain -- but no formal declaration was given by either the American Colonies on England, or visa versa. You might argue that the Colonies did not have standing to declare war on anyone. If you consider that argument in reverse, even King George III did not see fit to consider declaration of war but rather issued a Proclamation for Suppressing Rebellion and Sedition in August 1775, having declared the American Colonies "in rebellion against the Crown" -- a rebellion is generally considered to be a civil war, and civil wars rarely involve a formal declaration of war as it was generally understood to be needed between two sovereign nations during the 1700s. The Colonies simply had no ground to stand on to declare war on anyone.
2. The American Colonies did not comprise a formal government -- the Declaration of Independence was simply a first step in establishing a government that would eventually earn international standing to take actions such as declaring war. Prior to July 1776 the American colonies had convened two meetings: The First Continental Congress meeting before the events of April 1775, and the Second Continental Congress meeting after April 1775. It's important to note during the First Congress most of the talk was about how to avoid war with England. The talk during the Second was although fighting had broken out in April 1775, talk was still not about declaring war, but rather about a "civil war.” That would mean any fighting between American Colonies and Great Britain would be looked upon by nations of the world as a war WITHIN the English government rather than a war BETWEEN two sovereign (distinct and independent) nations. You might cite a passage or two from the Declaration to illustrate the cause the Framers were arguing: when people are oppressed by government, those people have a natural right "among the powers of the earth" to declare themselves independent. Can anyone doubt their intent to deliberately avoid the appearance of declaring war in favor of issuing a declaration of independence?
3. Finally, what words are found in the Declaration related to war? Not many. You might argue that the Declaration asserts that — rather than merely war — independence of the Colonies is justified because Great Britain has refused for so long to recognize grievances presented by the Colonies. So, the Declaration argued that when a single nation (Great Britain) finds itself divided such that some of its people, having done all that is humanly possible to reconcile with the rest, have no choice but separation. (Incidentally it was this very argument that the Confederate States of America used in 1860 to declare themselves independent from the Union.) You might conclude with a thought that Americans and so many other nations of the world since 1776 have been fortunate that the Declaration was a statement of independence and the right of self-government, rather than simply a declaration of war. This last section of your paper gives you a chance to trumpet the wisdom of Our Founding Fathers as they expressed so magnificently in their words:
"When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."
War would follow certainly ... but you could argue that the Founding Fathers had a singular intention: not a mere declaration of war, but a statement for the ages that would move forward the striving of people everywhere on earth to fight oppression, and for the right to govern themselves.
Hope this helps. Best wishes.