I have been asked this question several times, today on facebook a CFS suffer shared her experience and an article. The two pieces of information resulted in my researching this post.
Experience: “Hi Ken, I’ve been using cannabis for pain and neuroinflamation management for some years now. After feeling a lot better in these aspects I’ve stopped using it and I’m missing some gut relieve I got from it so I decided to check its antibiotic properties as I remembered some traditional uses of cannabis (much less psichoactive in the past) were mostly because of them.”
Research: “showed potent activity against a variety of methicillin-resistant Staphylococcus aureus (MRSA) strains of current clinical relevance.” 
Staphylococcus aureus keeps showing up in connection with CFS and I view it as a probable maintainer of CFS. It also has many antibiotic resistant species. See this blog post.
- “The latter [cannabis] compound showed moderate anti-MRSa (IC50 10.0 μg/mL), moderate antileishmanial (IC50 14.0 μg/mL) and mild antimalarial activity against Plasmodium falciparum (D6 clone) and P. falciparum (W2 clone) with IC50 values of 3.4 and 2.3 μg/mL, respectively.” 
- ” CBD also displayed powerful activity against methicillin-resistant Staphylococcus aureus (MRSA), with a minimum inhibitory concentration (MIC) of 0.5–2 µg·mL−1 (Appendino et al., 2008)…. CBN demonstrated anticonvulsant (Turner et al., 1980), anti-inflammatory (Evans, 1991) and potent effects against MRSA (MIC 1 µg·mL−1). Pinene is a major component of Sideritis spp. (Kose et al., 2010) and Salvia spp. EOs (Ozek et al., 2010), both with prominent activity against MRSA (vide infra)…. Amongst terpenoids, pinene was a major component of Sideritis erythrantha EO that was as effective against MRSA and other antibiotic-resistant bacterial strains as vancomycin and other agents (Kose et al., 2010). ” 
Coagulation is the suspected cause of much of the neurological symptoms of CFS
- ” The study thus shows that Cannabis sativa and the cannabinoids, THC and CBN, display anticoagulant activity and may be useful in the treatment of diseases such as type 2 diabetes in which a hypercoagulable state exists.”
- “Blood glucose and fibrinolytic activity were significantly increased [by hashish].” 
There are no suitable studies on PubMed,which means that I cannot clearly recommend it. There is evidence that it could theoretically help because of it’s impact on MRSA and other bacteria as well as coagulation thus I do not have grounds to question it’s use. The CFS suffer experience is consistent with the PubMed studies above.
Talking with a CFS user that have used cannabis, I would suggest using a juicer and making a smoothie out of the leaves. The logic is simple, this will likely result in the best delivery to the gut.
Side-effects of positive results
The obvious ones are to try to get a full coagulation workup, especially for inherited factors. There may be better treatments.
Check for what Staphylococcus species that are in your system (mouth, bowel) – again, there may be better treatments, possibly ones that could lead to remission.