As far as I’m aware without the filter when anyone makes a phone call your internet connection will drop. As you;re not planning on making Voice calls on the line there shouldn’t be a problem at all.
There is no problem connecting the DSL modem directly to the wall jack.
A phone line splitter only needs to be used if you connect a telephone to the same wall jack as your DSL modem/router. No phone to be connected to this same jack? No splitter needed; no filter should be used; no harm done.
Typical installation for an existing home involves installing DSL filters on every telephone, fax machine, voiceband modem, and other voiceband device in the home, leaving the DSL modem as the only unfiltered device.
what is DSL ADSL/ADSL2 Splitter ?
A DSL filter/Splitter is an analog low-pass filter installed between analog devices (such as telephones or analog modems) and a plain old telephone service (POTS) line, in order to prevent interference between such devices and a digital subscriber line (DSL) service operating on the same line.
Without DSL filters, signals or echoes from analog devices at the top of their frequency range can result in reduced performance and connection problems with DSL service, while those from the DSL service at the bottom of its range can result in line noise and other issues for analog devices.
In the splitter that the OP is referring to: the modem side is unfiltered and is a direct pass through, the other side of the filter helps keep the analog equipment from interfering with the DSL connection.
The important things to remember are:
The Filter/Splitter (and your ADSL modem) needs to be connected DIRECTLY to the incoming exchange line and must NOT pass through an In-Line Filter first. All analogue devices/telephones are connected via an In-line Filter.