Will testing my fiber to ANSI/TIA-568-C guarantee the application working?

No.

What it will guarantee is the workmanship of the installation. It is the design of the cabling system inconjunction with the testing that guarantees the application(s) working.

In reading Section 1 of ANSI/TIA568-C.0, it states:

"The diversity of services currently available, coupled with the continual addition of new services, means that there may be cases where limitations to desired performance occur. When applying specific applications to these cabling systems, the user is cautioned to consult application standards, regulations, equipment vendors, and system and service suppliers for applicability, limitations, and ancillary requirements."

It further goes on to say in Section 3.7

"Cabling lengths are dependent upon the application and upon the specific media chosen (see annex D). Specific premises cabling standards (e.g., those listed in the Foreword) may specify additional cabling length limitations.."

For example, 10GBASE-SR is limited to 26 m on 62.5/125 µm with a MBW of 160 MHz.km. Even though the ANSI/TIA-568-C permits up to 2,000 m in the backbone,  it clearly informs the user that they must take into
account the application requirements. For 10GBASE-SR using 50/125 µm with a MBW of 2,000 MHz.km, the supported distance is increased to 300 m. The supported distances can also be found in the DTX CableAnalyzer Limit Lines document by clicking here.