The answer is no. The Torah gives no such assurance.
The Laws of Noah are the bare minimum of tolerable behavior in human society. It is not a standard that one should aspire to or that can perfect the individual or the world. We do not teach that those who do not enter the Torah-covenant are condemned to hell or that those who are careful to keep only the Laws of Noah will not have a place in the World to Come. Rather, we emphasize that the belief that those who keep only the Laws of Noah are assured a place in the World to Come is a Rabbinic concept that was not agreed upon by all the ancient Sages and which cannot be found in the Torah. We do not object to the now popular Rabbinic belief that one who keeps the Laws of Noah will have a place in the World to Come, if he does so out of devotion to G-d, with a desire and intent to uphold His commandments. This, however, is simply our opinion. It is not a concept found in the Torah. We caution people not to rest their eternal life on the opinions of men which do not carry the authority of Divine revelation, no matter how nice the opinion. We wish to ask non-Jews the question, ‘Would you rather base your eternal state on the explicit promises of G-d found in the Torah, or rest the outcome of your eternity on a disputed Rabbinic opinion that is neither found in the Torah nor given by prophecy?’
It is our understanding that the foundations of one's religious understanding should be based on and rooted in the Torah. The Laws of Noah, on the other hand, are not rooted in the written Torah, but in the words of our Sages who saw the Laws of Noah indicated in the Torah. However, the belief that upholding the Laws of Noah alone is sufficient to assure a person a place in the world to come is an opinion presented in the Talmud that is not indicated anywhere in the Torah. Shmu'el ha-Nagid explained:
Everything mentioned in the Gemara [Talmud] that does not directly deal with the act of fulfilling the commandments is termed agadata [...] It is important to know that all matters which our Sages established as law, in connection with the commandment transmitted by Moshe Rabbenu [Moses our teacher] who received it from the Almighty, cannot be augmented or diminished in any way. HOWEVER, the aggadic explanations they rendered of biblical verses were in accordance with their INDIVIDUAL VIEWS and the ideas WHICH OCCURRED to them. [...] we SHOULD NOT build upon them."
The words of Torah are the basis of our faith, not the speculations of men - no matter how great.
Want to know more about the Torah's universal relevance?
R' Yosef Eliyah