Yes, we will accept private channels.
As for our web app, it is only used for obtaining incoming liquidity through a public channel (with a max capacity of 9m sats) with the option of including a spending balance as well. Larger capacity channels woukd require manually opening the channel from our end.
If you'd like us to provide you liquidity through a private channel, please DM us here or on the Telegram app (@LNServer) as we can always work something out for you. 🙂