Through personal experience i would say yes. The E17 does do a decent job driving the HD598. Will it scale up with better equipment? Yes! You will hear a noticeable improvement moving up to asgard, pan am and lyr. Lyr is quite ooverkill for the 598. The Asgard is more that enough, as the gains after that moving up will not feel like a justified investment.
Go for better cans first, then get something beefier to drive them. You might consider a schiit magni and modi combo or pair your e17 with the e09k, if the itch to upgrade is such that it needs scratching. either option wont be a huge stretch for the price.
For disclosyre, I have no personal experience of the last three gadgets mentioned, only the ones mention at the start of my reply.
Your E17 is driving them more than enough. Some people say that the 598 up scales well with better equipment. This very well could be, but there is no reason to spend $300 on a new amp when the 598 is so easily driven. The gain will not be enough to justify spending all that money. You would be better off saving your money for a headphone upgrade and then maybe upgrading your amp down the line when you have headphones that really will benefit from it.
I have never owned any expensive amps, just use fiio's, but I think too many people on here exaggerate the benefits of cable/expensive amp etc upgrades with efficient headphones such as 598 that don't even need an amp, but do benefit some from a little amplification. Spending twice is much as the headphones themselves cost on tube amps and expensive DAC's is a money hole that can be easy for newcomers to get sucked into because so many people on this site make a big deal out of cable, amp, DAC, magic fairy dust, etc upgrades for not that expensive headphones.
Thanks for the input. Both of you are suggesting new cans first but my fear is I'll buy new cans that the E17 won't drive and will be unusable, or at least not sound up to potential, until I can afford an amp to go with them. You are right that I am itching to upgrade something. I've had my setup for a year and looking for that next step that won't cost me $1000+. Maybe I'll wait until I can afford a new amp and cans together. Lots to think about.
Any other suggestions appreciated.