Kirstin on Fullback and Friends | Speaking on behalf of undergraduates and graduates, seeking work experience, this could be in the form of an internship, paid and unpaid work experience, voluntary work and work-shadowing experience, the answer is YES!! However, my comments come with a but…..your speculative cover letter will only produce successful results, if you take the time to invest research time, identify your skills set, unique selling points, personal and professional achievements, and this is very important what type of opportunity you are interested in.
A speculative cover letter is just as important as a tailored cover letter for an advertised position. You need to convince the employer that you have qualities and experience that will add value to a team/company. Just asking them for the opportunity to work for them will not suffice. So a balance of confidence (not arrogance), genuine interest in the company, sector/profession, with a positive summary on what you could bring to the company would be a good place to start.