"profoundly relevant" is correct and usable in written English.
You can use it when you are describing something that is very important or relevant to the discussion. For example, "Her experiences were profoundly relevant to the discussion we were having."
"The Lowry that we think we know is profoundly relevant.
9. War and the Iliad by Simone Weil and Rachel Bespaloff Written just before and during the second world war, these two long essays unearth a set of moral teachings antecedent to the Gospels, estranged by history but profoundly relevant to our time.
And it's profoundly relevant today.
This imperative is profoundly relevant in our era of increasing economic inequality.
And Kehinde Wiley recasts Old World masterpieces in contemporary terms made particularly and profoundly relevant by Obama's achievement.
Think about what happens when a graduate student, for instance, who trusts her advisor most in the institution, cannot safely tell her about a profoundly relevant experience within the context of her education at the institution?
IT management relies profoundly on relevant information which enables risk mitigation or cost control.
Despite of its excellent properties, the complex nature of multicomponent of gum arabic may act as an obstacle to understand profoundly its functionality and relevant mechanism in applications.
Labor may join us as a full partner in accomplishing this goal or the union may assume a hostile stance that might have been relevant in a profoundly different era.
"[Seeking a CMP] in this case to keep secret that which has already been openly admitted by the relevant government agencies is profoundly shocking".
She said: "This attempt to keep secret what has already been openly admitted by the relevant Government agencies is profoundly shocking".
