Does Islam promote peace? As a Catholic, I cannot claim authority to answer the question. My limited knowledge of Islam can, however, serve to set the problem posed by such a query in relief.
First, it is a loaded question.
When English authors employ the word, “peace” they are more or less consciously wording a concept represented by the Christian political and theological authors with the Latin, pax.
Arabic is the language of Islam.
The Arabic word most often translated to English as “peace” is salaam, which is, like pax, a technical, juridical term.
In the Christian tradition, pax (peace) is the presence of “justice”. “Justice”, in its turn, is “the condition of concord in society” achieved through the “rule of law”. “Law” is a “dictate of reason promulgated by competent authority and ordered to the common good”. “Reason” is a peculiarly human faculty, by the proper exercise of which human nature may attain to an understanding of Divine ordinance.
Salaam, on the other hand - and as far as I understand it - refers to the state of absolute submission to the manifest will of the one God. Now, “submission” in this case renders the Arabic word (another juridical term) islam, from which the Muslim religion has its proper name; the Arabic for “one God" is Allah, and the Arabic for “manifest will” is Qur’an, which is also the name of the Muslims’ holy book, often transliterated as Koran.
In any case, the Qur'an is the source and ultimate authority in and for law under Islam - for it is the revelation of the Seal of the Prophets, Mohammad.
Peace, according to the Muslim religion, is the absolute rule of Islam, or absolute submission to the will of Allah, as made manifest through His revelation, which is Law.
It would seem to follow, therefore, that there is no salaam where there is no islam, no “peace” outside the “complete subjection of each and every living person’s will, to the will of Allah as made manifest in the Koran”.
In other words, there can be no “peace” until everyone living has submitted to the dictates of the Muslim religion. Once the Law has been proclaimed, to refrain from an act of submission is, quite literally, to place oneself outside the law, i.e. to be an outlaw.
In the Christian tradition, peace (pax) is the presence of justice, which is the condition of social concord through rule of law, and that law is the perfection of reason (ratio), by which human nature participates in the Divine order.
There seems, therefore, to be little to justify translating both the Christian pax and the Islamic salaam with the English “peace”.
“Law”, after all, is for Christians the participation of human reason in the Divine order, while for Muslims, “Law” is ultimately the manifestation of Divine will, a will that one cannot hope to understand and to which one must only submit.
The question whether Islam is a religion of peace is therefore not even a real question: it only seems to be capable of being raised because of an inappropriate use of a single word in English to translate two different words from two different languages, words that function as technical juridical terms in disparate and conflicting cultural systems.