Is heating dilute HCl dangerous?
Say dilute HCl is used to convert some alkaloid to salt form, then the alkaloid is dried with heat, would gaseous HCl be released in the process?


Likely yes, unless it's the limiting reagent in the reaction in question. Probably best to assume some of it will come off as gas - that's the safest approach, in my opinion.


  Is there a threshold concentration of the acid, below which, this would be acceptable from a safety point of view?


Yes, there are several metrics used by various authorities to determine what "safe" means. You'll have to decide which one (or ones) are relevant to your situation.

Here in the U.S., the Occupational Safety and Health Administration (OSHA) - which is under the Department of Labor - has published this information on hydrochloric acid exposure limits and hazards. 

In that linked document, several other agencies such as the National Institute for Occupational Safety and Health (NIOSH) and the American Conference of Governmental Industrial Hygienists (ACGIH) list permissible exposure limits ranging from 3 to 7 mg/m$^{3}$; the Environmental Protection Agency (EPA) given an inhalation reference concentration (RfC) of 2 mg/m$^{3}$, detailed here as the concentration above which (I'm paraphrasing) bad things start to happen.

Good luck on your project and stay safe.