Hello,
Yes, the FortiGate can handle this. Of course, it all depends on what kind of traffic load your core is already handling and making sure it's matched to an appropriate FortiGate.
In fact, this is the typical scenario for many of our clients and has worked out well for them.
For example, in tightly-integrated environments, we can have a client access resources on another VLAN seamlessly through their SSO login. Not to mention the greater visibility into inter-vlan traffic, plus the ability to potentially stop - and otherwise quarantine - internal malicious actors, all from a single interface.
The higher end FG's - not the ones with SOCs, but rather the ones with discrete NP and CP ASICs - will theoretically get the best, lowest-latency performance.
Please read the Hardware Acceleration guide in regards to models you expect to use:
https://docs.fortinet.com/document/fortigate/7.2.0/hardware-acceleration/448300/hardware-acceleration
(an example, as a newer or more appropriate guide for your FortiOS version might exist)
Consider that models like the 2000E will have a unique "NP-Direct" architecture which removes the internal switching fabric, yielding even lower latency. However, you must follow the guide since port banks corresponding to their respective NP units cannot talk to each other.
Also consider reliability factors as well: if your core is designed with HA in mind - and if this is a requirement of your organization - then you should consider an HA FortiGate setup (also consider models with removable PSUs and other redundancy features that match your current core's configuration, again, if it's a requirement of your organization).
From a personal anecdote:
A new client of ours from a few years ago wanted to achieve better control over their inter-VLAN routing and were very proud of their Nexus 9000 series chassis. Like you, they felt managing ACLs was tedious and lomited compared to policies on a firewall. During the discovery process, they kept stressing how high performance their core was and experessing skepticism that "a firewall" could keep up with this level of performance. While their core was certainly capable of hundreds of gigabits of routing, we spent a good deal of time analyzing traffic and noticed that most of their inter-VLAN traffic came nowhere near these levels. In fact, most of their routed traffic was straight up internet traffic, limited by their 10 gigabit primary connection (and gigabit backup). They had been oversized, and I'm sure somebody collected a sizable commission for selling such an overspecced core.
They wound up with a 2000E which was more than capable of handling all their needs and ultimately "proved" to management that their core was being largely underutilized considering the kind of theoretical performance it could deliver. Their IT management team enjoyed the ease of management and visibility, while they never noticed a single difference in performance.
Consider that in the old days, when most firewalls were just using commodity PC hardware, using such a device to do all your internal routing would definitely fall short of a dedicated router with its custom ASICs. The FortiGate platform really blurs this line.
Best of luck!
