Generally yes for adults — standard NyQuil contains acetaminophen (not an NSAID), so it works differently from ibuprofen and the two are commonly taken together, but you must follow the dosing on each label and check with your pharmacist.
Standard Vicks NyQuil Cold & Flu contains acetaminophen (650 mg per dose), dextromethorphan (cough suppressant), and doxylamine (a sedating antihistamine) — it does not contain an NSAID. Ibuprofen is an NSAID, and because acetaminophen and ibuprofen relieve pain and fever by different mechanisms, the NHS says adults can take ibuprofen at the same time as paracetamol (acetaminophen) if needed. The "don't double up" rule for ibuprofen is about combining it with OTHER NSAIDs such as aspirin or naproxen — not with acetaminophen. The main concern with NyQuil plus ibuprofen is therefore not an interaction between the two, but staying within the separate dose limits for each drug.
Acetaminophen: NyQuil already supplies 650 mg per dose, and the label warns of severe liver damage if you exceed the maximum daily amount or combine it with any other acetaminophen-containing product — so don't also take Tylenol or another cold/flu medicine that contains acetaminophen, and keep total acetaminophen under 4000 mg/day from all sources (less if you have liver disease or drink 3+ alcoholic drinks daily). Ibuprofen: stick to the label limit (up to 1200 mg/day OTC, max 6 x 200 mg tablets in 24 hours per NHS), take it with or after food, and watch for stomach pain, heartburn, or signs of GI bleeding (black/tarry stools, vomiting blood) — higher risk if you're older, have a history of ulcers, take blood thinners, or have kidney/heart problems. Separately, NyQuil is sedating (doxylamine) and its label says to avoid alcohol; don't drive until you know how it affects you. If you're pregnant, have liver, kidney, heart, ulcer, or asthma issues, take other prescription medicines, or are unsure, ask a pharmacist or doctor before combining them.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.