I'll answer this for you since I just saw this and thought I could help, might seem weird since it's such an old post hahaha. I'm an econs major btw so I think I can help.
- Would the Business Statistics major complement the Economics & Business Strategy major?
Certainly, although not as much as say an IT major that you were doing. Remember, economics in uni is quite theoretical and generally people find more utility in doing practical units than theoretical ones. A lot of people I know who are basically fluent in economic theory learn the theory by themselves out of interest. With that being said, I think business statistics and economics+bus. strategy are quite compatible with one another especially if you're considering governmental jobs.
- Would I be eligible to do a Bachelor of Commerce (Honours) in Economics from a Bachelor of Business as long as I maintain a high WAM?
Consult
this link for more details about BComm (Hons), but I'll summarise it for your case. The units you have to take was summarised in the link before, but it doesn't exist now. If you've done the right units and have a high enough WAM for those units (2nd year micro, macro, + a few 3rd year economics units) you should be eligible. You should also do ETC2410 as a one-off unit in Clayton, and I'm sure they're fairly strict on that. Just email the Honours coordinator and see what you need. I remember the bar for BBus students are higher, at like 80+ than the usual 70+ for BComm students.
- Is doing a Bachelor of Business as compared to a BECon or BCom a disadvantage when applying for graduate roles or internships at places like the RBA or Treasury?
Ideally you should aim to do BComm (Hons) in Economics/Econometrics as these graduates are more highly sought after than anything else, but with the right results and experience in the different things that might assist work in the places you've mentioned (programming and analytics) it really doesn't make a difference, so don't panic and good luck!