If you're just looking at it as a mass trade, then yes, you will definitely get a mass savings by replacing a portion of your propellant with a bag full of nylon. Depending on your speed, the nylon can have a much higher "Isp" than the rockets.
However at the system level, there are other things to consider besides mass. First, parachutes are not "hyper-reliable". You need to consider the consequences of parachute failure, which is why you usually see three of them in a cluster on crewed vehicles. (Soyuz is an exception with one large parachute, though there is a smaller backup parachute you don't see. The single Soyuz 1 cosmonaut died on impact due to both parachutes failing.) Second, if you're doing a propulsive landing for the last bit, then you may need to get rid of the parachute and also make sure that it doesn't then interfere with the landing. Third, you wouldn't reuse these kinds of parachutes, so while they are relatively inexpensive for space systems, it does cost more to replace the parachutes than to refill the tanks, and they take a fair amount of integration time due to the care needed in making sure that the rigging will deploy as intended. Filling tanks, even with hypergols, can go pretty quick. As noted in another answer, you are more at the mercy of the winds while on a parachute, so if you are targeting a very small landing location (e.g. a pad), then you will have more correction to do once you go propulsive, and will need more altitude in which to do that. Or you could have a steerable parachute, which has its own efficiency and reliability issues, and you would still be correcting at the end with the rockets.
Even with all that, if you really need the down-mass capability, you may find yourself working to solve all those problems in order to incorporate a parachute system and reduce mass. But if you're in a happy place for mass, then you would want to avoid the complexity, cost, and reliability issues of parachutes.