Call of Duty as a franchise has generally kept progression across its modes separate from each other. Weapon and perk unlocks in multiplayer wouldn’t have an impact on Zombies, and campaign unlocks would remain constrained to that mode. However, in Call of Duty: Modern Warfare, Infinity Ward will have universal weapon progression across all modes.
So if you want to unlock the weapons, attachments, camos, and so on for a gun without playing multiplayer, you can do just that. As per a report on CharlieINTEL, progression will apply across multiplayer, campaign, and the as-of-yet unrevealed co–op missions. The real question is how new weapons, usually introduced in post-launch events and updates, will factor into this.
Call of Duty: Modern Warfare will release on October 25th for Xbox One, PS4, and PC. It’s the first game in the series to have cross-platform multiplayer. A new engine is also being employed with support for 4K HDR, and there won’t be season pass. There is no Zombies mode either, though.