Absolutely you can keep those funds. We were in the exact same situation, holding DGEIX at Fidelity, as well as a few tax-exempt bond funds, managed by an advisor. I sold off the bonds and enough of the DGEIX holdings in order to net out the gains and losses, and transferred that money to Vanguard. That still left me with a little under $100k in DGEIX at Fidelity, which I haven't touched and probably won't until 1) we see significant market drop to minimize capital gains taxes or 2) I retire and sell off what I can while staying within the 15% bracket to get 0% long term capital gains.
You will have to decide how you want dividends handled. I initially turned off automatic reinvestment, and would send them to Vanguard, but eventually decided to turn reinvestment back on as there were a few times where I was slow to make the transfers out and to Vanguard (and I think maximum time exposure to the market outweighs the relatively small ER difference, which is around 0.33, 6.5x VTSAX), but it does have some advantages, I can't purchase myself except by dividend reinvestment, and I also keep it around in order to compare the rest of my holdings to it, to help persuade my wife that firing the advisor was a good choice. I'll admit, not great reasons, and like I said, once timing allows me to dump significant portions of it, I will, but keeping dividends reinvested just made my life easier all around with little real downside.
