Good news
By going to any computer connected to the internet and asking a world time server, "What time is it?"

• Or access to any GPS device would also give you the time / date.

It would be difficult to not discover the date if you had access to a computer of that era.

Bad news
However, 100 years is a loonnnggg time for technology. It's likely the communications protocols for wireless and wired connections would no longer work. In fact, the bandwidth for the devices could have changed (e.g. the protagonists wireless phone might emit signals in a band now restricted for military use).

But just sending and receiving signals doesn't mean the future devices will speak to the protagonists devices. Heck, data storage technologies, data storage formats, operating systems, file systems, file formats, computer languages, etc. will likely have undergone 1 or more drastic / dramatic changes. The underlying technologies, the strategies for doing these things, and the programming to control them will all have changed too much for 100 year old implants to do much with the future tech.

Imagine interfacing a Cray computer with a WWI era navigation plotting table on a ship, it just doesn't work.

How would a current era computer speak to one that no longer recognizes TCP/IP for network connections?

Furthermore, I remember using computers 40 years ago. At that time I could type faster than the computer's network connection could transmit data. Current data transmission speed might be something like 40,000,000x faster than the communications of that era. It is likely the protagonists "implants" won't even know they're being talked to.

Good news
By going to any computer connected to the internet and asking a world time server, "What time is it?"

• Or access to any GPS device would also give you the time / date.

It would be difficult to not discover the date if you had access to a computer of that era.

Bad news
However, 100 years is a loonnnggg time for technology. It's likely the communications protocols for wireless and wired connections would no longer work. In fact, the frequency allocated for the devices could have changed (e.g. the protagonists wireless phone might emit signals in a frequency now restricted for military use).

But even sending and receiving signals in the proper radio frequency doesn't mean the future devices will speak to the protagonist's devices. Heck, data storage technologies, data storage formats, operating systems, file systems, file formats, computer languages, etc. will all likely have undergone 1 or more drastic / dramatic changes. The underlying technologies, the strategies for doing these things, and the programming to control them will all have changed too much for 100 year old implants to do much with the future tech.

Imagine interfacing a Cray computer with a WWI era navigation plotting table on a ship, it just wouldn't work and it is unlikely that any amount of reprogramming would enable the devices to adopt the new standard.

How would a current era computer speak to one that no longer recognizes TCP/IP for network connections? How would you reprogram an Ethernet controller to speak to a wired connection that doesn't use Ethernet network standards?

Furthermore, I remember using computers 40 years ago. At that time I could type faster than the computer's network connection could transmit data. Current data transmission speed might be something like 40,000,000x faster than the communications of that era. It is likely the protagonists "implants" won't even know they're being talked to and if they detect the signal no amount of programming would enable it to make sense of what its receiving.

Imagine a multispectral network connection using many colors and polarizations of light to transmit data. Unless you had a future receiver capable of detecting and decoding such a message your hardware might only be able to tell there is a signal. Since it will miss most of the message (that transmitted in other frequencies and polarizations), there is zero chance of making it work.