Certainly would be light enough. Once upon a time - 20 years ago? - I flew to Michigan for a planned visit and to take in a fishing trip to the Au Sable River. Packed a bag for check-in, had a little hang-over-the -shoulder carry aboard. Also took my two piece 8' 5wt (enclosed in a special travel tube just made for travel) and checked that in with the big bag. What happened next was not all that uncommon for air travel ... I arrived but who knows where the checked in bag and the rod tube went (had one of those change plane/airline trips!). Anyway, the fishing trip was planned for the next morning and so I made a special trip to a local K-Mart to buy trousers, a sweat shirt and a Martin 8' 5/6wt rod kit that came with rod, reel, line, backing; and the reel was a Martin Model 60.
Turned out to be a good fishing trip and I was pleasantly surprised how well that inexpensive 3-piece rod performed. I've had a couple other Martin reels over the years but they were more upscale then the Model 60. But the bottom line to your question is the reel worked for that 5/6wt rod & line so I should think it to be adequate for the 4wt, certainly light weight enough and the right size.