No. They follow normal restrictions for their Troop Type and any special rules that would normally apply to that unit or weapon.

In most cases it'll be fairly obvious which troop type category a model falls into, but as troop type is essentially an extension of the characteristic profile, you'll find that information in the relevant Warhammer Armies book. Most units in Warhammer conform to one of the following types. Some particularly unusual units are literally in a class of their own - we call these 'unique' units. Such troop types have special rules that govern them and only them, clearly stated in their entry. 

Warhammer Armies Project: Unofficial 9th Edition (v2.2)

Troop Types - Frequently Asked Questions
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If unit has a rule or weapon that 'fires like a (stone thrower/fire thrower/cannon/etc)' but the troop type is not a War Machine, is it still subject to Slow to Fire or Move or Fire?
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Are characters on ridden monsters considered just one model?
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Troop Types - Frequently Asked QuestionsURL Copied!

If unit has a rule or weapon that 'fires like a (stone thrower/fire thrower/cannon/etc)' but the troop type is not a War Machine, is it still subject to Slow to Fire or Move or Fire?URL Copied!

Are characters on ridden monsters considered just one model?URL Copied!

Troop Types - Frequently Asked Questions
URL Copied!

If unit has a rule or weapon that 'fires like a (stone thrower/fire thrower/cannon/etc)' but the troop type is not a War Machine, is it still subject to Slow to Fire or Move or Fire?
URL Copied!

Are characters on ridden monsters considered just one model?
URL Copied!