Lets consider some things:
- Your example states 300k/h
- The current bond price is roughly 12.3 Million gold (at time of posting).
- One bond is 14 days of membership, or 336 hours.
At 300k/h, it will take about 41 hours to make 12.3 million gold (simply divide 12,300,000 by 300,000).
You should also note that:
- Redeeming one bond gets you 14 days
- Redeeming two gets you 29 days (1 extra day compared to trading in one bond at a time)
- Redeeming three gets you 45 days (3 extra days compared to trading in one bond at a time)
If you can hold out for 123 hours grinding away at your 300k/h example, you'll earn enough to buy 3 bonds, earning you about a month and a half of membership!
However, this is in a perfect scenario, where all time is spent making gold and the price of bonds are fixed which is not the case. I'm sure you don't plan on playing the game 41 hours straight let alone 123 hours to earn enough gold. Realistically, lets say you play the game for 6 hours a day (which sounds generous). The other 18 hours of the day you'll be doing other things (sleeping, eating, working, school, whatever it is). At that rate, it'll take you ~6.83 days to make enough money for 1 bond (164 hours)!
Now, once you redeem your one bond, you'll have 336 hours of membership time. Sticking with your 300k/h example, 336 - 164 (the "realistic" amount of hours to make enough gold to buy one bond), leaves you with 172 hours (~7.17 days) of membership time left to do other things.
At this point, you may be thinking, how can I speed this up? The obvious answer: make gold faster! The Wiki has multiple ways on how to make money, and they break it down into hourly rates as well. However, this is the part of the question that starts to become opinionated. I can't quite recommend a good method here, since it depends on too many things, such as how much money you currently have, your current skill levels, the current quests you have completed, if you are currently F2P or P2P, etc.
If I had to choose from the linked list above, I would choose fletching headless arrow shafts (700k/h), or killing guards (461k/h) since both of these require low skill levels to do, relatively little gold, and a F2P player can do these activities as well.
So to answer your question of is this possible? Certainly. You just have to be willing to put the time and effort into it.