I'm not going to lie, it seems plausible. First off, we have no idea what the ARKON program is or might be, nor do we know what this Ark ship may be capable of. Based on in-game dialogue, we know that the Asari were tossing around the idea of replicating the technology behind Mass Relays, and we know for certain that the Protheans succeeded. Between the two, it's entirely possible that maybe some data from Illos was recovered and used for this ARKCON, especially when we know that Salarian researchers were studying all that had been left behind according to news reports in Mass Effect 2. Or we could simply re-purpose a preexisting Mass Relay to shoot the Ark into the Andromeda Galaxy.
Without Mass Relays, the fastest FTL speed possible allowed the Reapers to travel 30 light-years in a 24 hour period. After doing some minor math, I discovered that it would take roughly 228 years to reach the Andromeda Galaxy at the same speed. However, the whole point of the Mass Relays was to convert a journey that would take years or centuries with FTL drives into a few hours or a day at most. Proportionately speaking, if we can travel from one end of the Milky Way to the other in less than a day -- a journey of 100,000 light-years -- we could make the 2.537 million light-year trip in ten solar years.
Also, never underestimate what writers can come up with to justify anything.