I'd like to see a definitive answer to this one from Matt Sprange, but I as I read it: if you want to use the RuneQuest logo on your new product, then no, no you can't. RuneQuest Logo Licence v1, point 11:
11. Gaming books produced under this agreement may not detail the process of generating and assigning scores to Characteristics. In addition, the terms used for Characteristics (Strength, Constitution, Dexterity, Size, Intelligence, Power and Charisma) may not be changed. They may be abbreviated to STR, CON, DEX, SIZ, INT, POW and CHA respectively. Readers may be referred to the RuneQuest (TM) Main Rulebook in order to generate and assign scores to Characteristics.
If you wish to include the RuneQuest logo on your product, the licence states you "may not detail the process of generating and assigning scores to Characteristics". Therefore any alternative process looks as if it will break this term of the licence.
Just like d20, the way to get around this is not to use the logo, such as Mongoose themselves have done on their more recent d20 games.
If you want use of the official logo and trademarked terms, you have to help sell copies of the core rulebook
If you want to create a complete standalone game using the RQ SRD as a base, you should be able to do that and not use the logo or refer to any trademarks (other than within section 15 of the OGL, of course).